Yes
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Awarding experience as entire levels instead of keeping track of the experience points is an easy and reasonably popular alternative way for character advancement. The Dungeon Master's Guide has a small section devoted to this variant, "Level Advancement Without XP", on page 261.

You can award levels on a per-session basis, or based on campaign progression. In my own DnD 5e games, we use the latter: whenever the players complete an adventure or a particularly dangerous part of one, they gain a level at the end of the session.

An advantage of this method is that it is possible to fine-tune and pre-plan the experience progression very easily to suit your tastes, whether that means a swift "zero-to-hero" ascension or an extended adventuring on the lower levels. There's also less need for bookkeeping. A possible disadvantage is that the progression can feel arbitrary and less objective than XP, and removes the immediate experience reward for succeeding in combat or other challenges.