It's really weird to me how completely disconnected the main level-up options in the Dungeon Master's Guide are.
Here's the text from 2014 DMG about leveling up your characters based on how many sessions you'd played:
A good rate of session-based advancement is to have characters reach 2nd level after the first session of play, 3rd level after another session, and 4th level after two more sessions. Then spend two or three sessions for each subsequent level. This rate mirrors the standard rate of advancement, assuming sessions are about four hours long.
The 2024 DMG adds a couple little sentences about adjusting this for length of session and accomplishment, but sticks to the general formula above.
So how does that compare to XP gained from combat encounters, which I will note is the default system that the game largely assumes you are using, and which the various rulebooks (2014 and 2024 DMGs, and also Xanathar's Guide To Everything) spend a lot of time and word count (and math) hashing and rehashing.
I'd say that if you're tracking XP by combat it will take you at least 2, and more likely 3 sessions to get to level 2. I've also seen it take a lot more than that, especially with cautious players, or with those still learning the system or playing a new class for the first time.
I'm not saying it's in any way a problem that the recommended progression rate for leveling-up by session is two to three times the speed of advancement if you did the XP math, but it is odd to me that this wide a gap exists without them mentioning it in any of the books that present that math.
Supporting XP math and book references can be found below the fold, along with a fair amount of rambling.
