10:15 AM PT -- A source with direct knowledge tells TMZ that Avril Lavigne doesn't have a new love interest here in Nate Smith -- instead, they're just good pals ... skate buddies, it seems.

In terms of why they were even together in the first place ... we're told it was to just discuss future music projects, and nothing more.

Avril Lavigne is getting back to her roots -- and by that, we mean she's hopping on a board and hanging out with skater boys again ... like this fella, who seems to have caught her eye.

The punk rock singer enjoyed a date night Monday with TikTok country star Nate Smith ... with the both of them hitting dinner together at Catch in WeHo -- and then hitting the streets right after for a little truck ride around L.A., where they boozing in the back.

Their post-meal palling around is definitely the opposite vibe of their fancy meal ... which is one of the nicer restaurants in L.A. If anything, this is the sorta thing you do in a small town -- along some backroads and whatnot -- and yet ... here's AL letting it all hang out!

At one point in their drive, they stopped at a gas station ... where she and Nate hopped out with skateboards in hand, which they mounted and tried riding. Emphasis on "tried." 😅

Take a look for yourself ... they both seem to struggle a bit, but did end up rolling around for a little bit -- and in the end, it looks like Avril might've been the one who had a tad bit more skating experience. Go figure, right?

Props to Nate, though ... he definitely puts his best foot forward, no he's just gotta kick and push. Like we said -- this is like a scene straight out of Avril's 2002 song/music video.

Also, from the looks of it ... she's pretty into NS here -- signaling that she's officially over Tyga and ready to explore new pastures in the dating scene. BTW, in case you didn't know ... Avril's had a lot of famous exes over the years -- with big names you'd certainly recognize.

Just to name a few ... Brody Jenner, Mod Sun, Pete Jonas, Deryck Whibley, Wilmer Valderrama, Chad Kroeger, Jesse Colburn, Brandon Davis, Phillip Sarofim and a couple others.

At the moment, Nate's got her attention ... and he's already leaving a good impression. The dude definitely knows how to hang -- he just might need to work on his board skills a bit.