When Marty McFly goes back in time (thats when the plot starts) during his absence in the timeline where he first left wouldn't his parents be thinking "WHERE THE F IS MY SON?" lol...
To break it down further - while marty is in the carpark heading back in time he stays for awhile (the whoke movie)... wouldn't George and Lorraine wonder where he is after being gone or "missing" for awhile. Fair enough when marty goes back to the future (carpark) george and lorraines timeline wouldn't have changed. But while he was gone surely they would of been panicking lol
There's nothing to solve. As far as the people in 1985 are concerned, he never left. As a matter of fact, because he came back 10 minutes earlier than he left, there were 2 Martys coexisting in 1985. A week passed for Marty, not everyone else. That's why Jennifer said "You're acting like you haven't seen me in a week." Technically, Marty is actually a week older than he was when he left, but everyone else is the same age.
Since the time-travel depicted in this movie can only be fiction then we can never know the answer. I see you already have one answer, that one would work.
Another would be that time continued in 1985 normally and Marty's family wondered for most of a week where he was. Then when Marty facilitated George standing up to Biff in 1955 that changed the timeline going forward such that the family Marty had in 1985 no longer existed and when he returned to the "new" family in 1985 such a short time had elapses that they didn't notice anything.
There are other explanations, let's see if others will come up with some of them.
I was going to follow up my answer with "If you assume time runs concurrently..." and explain essentially what you did, but I decided I didn't want a tl;dr situation. Ultimately, time travel can get really messy if you think about it too much.
during his absence in the timeline where he first left wouldn't his parents be thinking "WHERE THE F IS MY SON?
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The passage of time after Marty's departure from the original timeline (TP1985) is inconsequential because that timeline is replaced entirely by a new tangent (LP1985) as soon as Marty travels to 1955. When Marty returns to LP1985, he does so just before the time he originally left, so no one would have noticed he was missing at all.
while marty is in the carpark heading back in time he stays for awhile (the whoke movie)... wouldn't George and Lorraine wonder where he is after being gone or "missing" for awhile.
When you say carpark, I am assuming you mean the parking lot at Twin Pines Mall. It was after 1AM. George and Lorraine were sleeping and had no idea Marty was gone. Even after the new timeline tangent is created upon Marty's return to 1985, Dave asks if he'd slept in his clothes again. George and Lorraine return from playing tennis shortly thereafter and likely assume the same thing.
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There is a theory about time where all points in time happen concurrently; so it's not impossible that the original, unaltered timeline that Marty left from, continued on from 1985, for a relative flicker of a moment. Under such circumstances, yes, George and Lorraine would wakeup the next day, and Marty would not be there. Since he had plans to go camping that weekend, it's possible they would conclude he found some other means to go, since the McFly's car had been wrecked; and at best they would not have cause to worry until he fails to come home by the end of that weekend. Lorraine starts to worry, telling George she can just sense something's wrong, as she finishes her third Jack Daniels and Pepsi; while George tries to remain optimistic that everything's fine.
That's when the FBI shows up. Two special agents inform the McFly's about something they had been keeping under wraps the last two days. An old man had been found shot dead in the parking lot of Twin Pines Mall; the official report released to the media was that it was a carjacking gone wrong, probably gang related, but the FBI had reason to believe that this elderly gentleman, one Dr. Emmitt L. Brown, had ties to Libyan extremists, who were suspected of being involved in the disappearance of a case of plutonium. The bullets used to kill Dr. Brown were consistent with machine guns this group of extremists are known to have. They have radiation readings of the parking lot have confirmed the likely presence of the plutonium in the immediate vicinity of Dr. Brown's murder; and it's believe that Dr. Brown was killed during an exchange gone wrong. About a hundred yards or so from where Dr. Brown's body was found, the combined wreckage of a photo-hut and VW bus; inside of which were the bodies of two extremists the FBI had been monitoring. They died from trauma of the impact. The stolen case of plutonium was recovered, but two vials were missing; and it was believed those vials were smuggled out in another vehicle presence, caught briefly on exterior security cameras, that recorded a high speed chase between the VW bus and a heavily modified Delorean DMC, shortly before what appeared to be a high energy EM burst shorted out the system. This has lead the Bureau to lean towards the theory that Dr. Brown tried to double cross the Libyans, and keep the plutonium for himself; and that an accomplice made off with the two missing vials. In running down a list of current known associates to Dr. Brown, only one name came up - Martin George McFly, age 17.
George and Lorraine admit that their son did know Dr. Brown, and that he had hired Marty about a year earlier as a "lab assistant," to clean his laboratory space, and occasionally walk his dog. The agents ask if that's the same "lab" space located at such-and-such address, located next to a Burger King; which is in fact, not a properly zoned lab or residential space, in spite of Dr. Brown using it for both. Investigating that space found it in a state of disarray, also noting that trace radiation had been detected there as well. When asked where their son is, Lorraine asserts that her son had planned on going camping with some of his friends; while George nervously chimes in that, that was entirely true, as he had been planning to go camping with his girlfriend, but when he hadn't returned home, George had called Jennifer and she said she hadn't heard from Marty since he called her at her grandmothers to tell her the care was wrecked. Lorraine immediately attacks Jennifer's character, saying she never trusted her, and that she's probably lying; and that Marty is probably fine, and will be home soon. "He's always worrying needlessly, this one," she tells the agents, referring to George.
Of course Marty doesn't return, and the FBI continues its investigation; interviewing some of the other people in town who knew Marty. His principal had nothing flattering to say, other than that he's not surprised that Marty's association with Dr. Emmitt Brown has lead to him being interviewed by the authorities. George's supervisor, Biff Tannen, attests that Marty was a "butthead," and that if they think he's involved in something possible treasonous, he wouldn't be surprised. The news media gets wind of this, and a national debate erupts about whether this teen is a homegrown terrorist or a missing youth caught in the crossfire, whom people should be looking for, to bring him home. Folksongs are written about Marty, based on speculation that he was actually trying to protect his country by keeping the plutonium out of the hands of terrorists; before succumbing to radiation poisoning and dying somewhere in the desert. Others think he's hiding in a cave, planning to use the plutonium in a domestic nuclear strike; something becomes it's own sort of folk legend among domestic and foreign extremists. To some militant Americans, he comes to represent a true hero, taking back the power that Uncle Sam had been keeping to itself since World War II; while terrorist outside the US see Marty McFly is everything to aspire to - the one who got away, who holds the power and pulled on over on the capitalist dogs. That's when terrorists begin attacking in his name; Marty's image is used the world over for propaganda, that gives rise to a dystopian police state, that last a thousand years - until the house of McFly is uncovered by archeologists. It had been lost in the atomic cola wars of '87, but there they find a treasure trove of memorabilia belonging to The McFly; including an archaic form of analog media called the "cassette tape". Scientists were able to devise a way of pulling the contents off of it, to learn that this was a "demo tape" of Marin McFly's band, the Pinheads, playing a song that surprised everyone. Instead of lyrics about death, destruction, anarchy, it was about love! About the power of love, how it makes one man weep, makes another man sing; and that you don't need money or fame or even a credit card to ride that train. Love, Marty preached, makes the world go round; and overnight the world was inspired by the man once believed to be a ruthless despot, but was really a visionary. Soon a new era of peace would prevail and last for ten thousand years.
And in the next blink of an eye, Marty arrived in 1955, and prevented his dad from being hit by a car; erasing everything that would happened from that moment on, and placing the future into a state of flux, until he made further alterations that align it closer to the future, but never back the way it would have been if he remained missing.
"What's the matter, sir? It still tastes like cream of corn." "Except it's deviled ham!"
Isn't he only gone overnight? He goes out after dinner to meet Doc and then shows up in the morning. Maybe they noticed that Marty didn't sleep at home, but perhaps they were okay with that and knew that he'd spend time at Doc's
He returns the next day, in an alternate timeline. From the prospective of the original George and Lorraine, to any extent that the original, Twin Pines Mall timeline might have continued, Marty McFly never returned home.
"What's the matter, sir? It still tastes like cream of corn." "Except it's deviled ham!"
Once the Doc is saved by his bullet proof vest, he drops Marty off at home only a few hours after he left (maybe less than one hour).
I know it is now a different timeline, but even if it wasn't, he was only out of his parents' house for a short time - all be it, in the middle of the night.