Taylor Swift & Travis Kelce Hold Hands During Dinner Date in NYC

Taylor Swift and Travis Kelce have shown flashes of PDA, but never quite like this -- namely, the first time we've seen them hold hands in public ... and TMZ's got the video.

The hot new couple hit the town in NYC Saturday night ... strolling into Nobu with nobody else but them, and some security guards in tow. In other words, it was date night -- which was evidenced by the way they were grabbing on to each other, and TK leading the way.

On top of the romantic gesture here, eyewitnesses tell us they were also cuddling at their table. On the way out ... Travis proved to be a gentleman, putting Taylor's coat on for her.

Remember, we already told you they had plans to spend the entire weekend together ... y'know, in light of Trav having a few days since his team got their game over with on Thursday. His brother, Jason, plays with the Eagles in nearby New Jersey tomorrow -- so it would appear they're in town for that and will most likely attend together. Big step, indeed.

Just yesterday, there were a bunch of SUVs parked outside of Travis's home in Kansas City ... so yeah, TayTay spent the night. Later Saturday, her private jet took off from KC and landed on the East Coast. Now, they're gallivanting around the Big Apple together.

Like we said, this is the first time we're seeing them straight up hold hands like boyfriend/girlfriend -- before this ... we saw them cozying up at a Kansas City afterparty.

Of course, everybody also saw them drive away together in Travis's muscle car convertible.

The only other time we've seen them in the same picture frame was when someone recorded them leaving the stadium on that 1st game she went to in-person a few weeks ago ... but they weren't touching then. Now, they totally are ... it's safe to say, they're dating.

TBH, the way Travis literally manifested this thing out of nowhere it's pretty inspiring. He literally just recounted a time he attempted to shoot his shot (to no avail at first) ... and just like that, he will a relationship into existence. Talk about the power of the universe, huh?

Of course, the NFL itself has obviously been eating this pairing up like nobody's business ... they've been loving all the hype and attention it's getting -- not to mention the ratings.

Assuming these two come out to tomorrow's game, FOX is in for a swarm of eyeballs. It would mark the the first time Trayvis would be in a private suite, side by side.