I give you a couple of bucks and I hope that you're going to use this money to get yourself ahead so you don't really need the money anymore.
Who said anything about using the money to get oneself ahead? Or getting to the point of not needing it anymore? Neither "need" not "getting ahead" are part of the equation. You're still tjhinking of this in terms of "program for the poor".
To me the goal is to make it so people don't need this money anymore, because in an ideal world the program doesn't even exist and people just provide for themselves without the government getting involved
No advanced human society has ever even sniffed this ideal It's an impossibility. Might as well plan for what human societies actually exist.
Again - what's the point of the program if it isn't to alleviate poverty. It would be a lot more efficient, less costly, and entirely fair for the government to eliminate all of the programs and give nothing to anyone. If we're not worrying about alleviating poverty, that's my preference.