Will a top journal at least read my introduction? I'm currently preparing an article for a very good journals in mathematics (AMS, Acta, Advances, etc.). I have never had a result worthy of these journals until now.  I would like to know whether I can count on the editors to at least read my one-page introduction before making a decision. Or could they stop after the abstract?  The reason I ask is currently my abstract is very short and gives zero background.  If someone were to only read it, they could undervalue my paper.
No, there's no such guarantee.  A top journal gets an awful lot of submissions, and you can expect them to be aggressive in rejecting papers which do not make a strong case for their importance, in the way that involves the least work for the editors.

If the editor, after reading the abstract, does not understand why the results would be highly interesting and significant, I would fully expect them to reject the paper without reading the introduction or any other part of the paper. (I can even imagine cases where they could make such a judgment by only reading the title.) As such, your abstract definitely should provide motivation for your results, such that a reader who is generally familiar with the area can see why they are of interest.

If your abstract just states the result ("we show that every snark is a boojum"), then it had better be such a well-known topic that every reader in the field would immediately know why it is of interest to know that every snark is a boojum.  If that is not the case, then your abstract should briefly explain why people should care, perhaps relating it to previous work.  ("Previous work of Smith showed that every reticulated snark is a boojum.  In this paper, we show that the assumption of reticulation is unnecessary, thus resolving a conjecture of Jones.")