Causality in Quantum Leap isn't 100% clear, but it does seem to have a rippling effect where the present is overwritten by the changes made to history and their effects on other events. Al witnesses the congressman change to the woman Sam had just leapt in to save, yet he's aware that history has changed (which could be a side effect of working at the project). Al himself disappears when the probability that his younger self would be executed reached 100%; and reappeared when the odds went down significantly, with the discovery of Chip's cigar in Bingo's car.
And yet, the effects Sam has on his own personal timeline didn't so far contradict the existence of the project or his leaping; Tom surviving Vietnam, Sam marrying Donna, even the brief window where Al died as an ensign and never got to meet Sam - Sam still builds Project Quantum Leap, and leaps back in time. Outright preventing his own initial leap though would arguably create a paradox that simply couldn't be sustained. By not leaping, he doesn't go back, which changes the changes he made to history; meaning he doesn't send the letter, so he does leap, which means he can send the letter, and so on, and so on.
A key component of this would be Sam needing to know the exact date he first leaped, or at least precisely enough to have the letter arrive beforehand. If his Swiss cheesed memory doesn't recall, he'd have to rely on Al and Ziggy; and Al is under orders not to provide Sam with any personal information he doesn't already know, and we do know there are some things Al doesn't tell Sam, that he doesn't remember on his own. Ziggy would arguably have some sense of the implications of Sam preventing his own initial leap, and impress on Al and others at the project the risk of allowing Sam to do that.
The bigger question should be; why not put the person Sam has leapt into, who's in the waiting room, into the accelerator, and leap them into themselves, sending Sam back to them?
"Our families are in there! Our, uh, mothers and... and tiny, tiny babies!"
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