I'm normally the biggest proponent of "toss it" on this board, but we're talking about meat that is not past its use by date and that OP can't detect any other obvious problem with. I would definitely not throw it out.
OP, if your concern is that even though you're cooking it before the use by date, you're serving it one day after the use by date, I don't think that's relevant. How long the food remains safe AFTER you've cooked it is a different question from how long it remains safe BEFORE you've cooked it. That is, if it is something that lasts five days after proper cooking in the fridge, it will last five days after cooking regardless of whether you cooked it minutes after the cow got slaughtered or minutes before the food went bad.