Josh Allen, Hailee Steinfeld Look Smitten On Romantic Dinner Date ...

Josh Allen and Hailee Steinfeld are having trouble keeping their mouths off each other in Mexico -- 'cause even at a lavish dinner earlier this week ... they were seen sucking face the entire time!!!

Just one day after the two put on a PDA show while taking a swim at their fancy Cabo resort ... the new couple was spotted getting in an oceanside meal -- and it, at times, got a little steamy.

In between bites, the two snuck in a bunch of kisses ... and there was even some heavy nuzzling and cuddling going on as well.

The NFL star and the "Starving" crooner have yet to publicly state they're an item ... but based on everything they're doing while on the out-of-the-country vacay, it's pretty clear this is more than just a fling.

The two were initially linked to each other back in May ... when they got a little snuggly at a sushi dinner -- and it seems things have certainly heated up since then.

Guess it's time to officially welcome Steinfeld to the Mafia, Bills fans!?