I had something slightly similar was 5-5:30am for potentially a handful of reasons but then became a habit (sounds like you may have a habit rooster too!) - what we did was check the routine like Amy has suggested, made sure to cap day sleep, made sure the room was dark, made sure he warm as that’s often a culprit for the early morning wake with the temperature drop, he was already self settling and then we started leaving him (as long as he was happy!!) - it took a few days and he started falling back asleep close to 7, then earlier then earlier then stopped waking, we now get 6am most days 🙏🏻 Another friend also used the method of leaving as long as possible until 7 then if they’re upset either standing at the door or over the microphone saying whatever you say to them at bedtime (eg it’s time to sleep goodnight we love you) and said it took 3 days and their daughter started falling asleep and they now sleep until 7 :) avoiding going in as they think it’s time to start the day
Have you tried like a 60 min nap consistently for about 7-10 days? Usually early wakes are due to undertiredness. And if you’re going between 45 mins to 3 hour nap inconsistently then it could potentially be messing with his sleep schedule. Any changes in schedule need to be tried consistently for 7-10 days apparently.
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How old and what’s your routine x