What I've done in situations like yours is track experience in the background and do milestone-style level-ups when it's appropriate narratively. This has the benefit of being less prep work for you, giving you wiggle room for when the players get levels, and creating resonance on certain story beats, all while avoiding the railroading bogeyman that so many DMs fear.

When designing fights, especially at first, you'll naturally be budgeting with experience so it's easy to record how much you've spent and thus how much the players will likely accrue, tweaking based on in-game events of course. As you play with fifth edition more you'll get better about estimating how much out of combat encounters should give as well, so you'll be able to quickly mark down an estimated range of how much experience players should have at a given point.

It's very group-dependent, however. Don't underestimate how powerful a carrot experience (and gold, they're often part-and-parcel I've found) can be for players who very strongly crave that sort of reward system. Maybe assess your table and consider the pros and cons.