Hey,
I used to have the same problem in the mornings, it ruined my energy for the whole day coming since i usually woke up around 6 in the morning and then went back to bed to sleep till 8/9, waking up even more exhausted.
I solved it by getting into a morning routine, started with doing 30 minutes of exercising right after i woke up(no matter the time), followed by a cold shower right after.
It helped me a lot, fresh start and more energy for the rest of the day.
It might take some time to get used to it but it will defenitely improve your sleeping pattern.
In case the cat keeps bugging you, i suggest you get a little door so he can go out when he wants?
Anyway, hope this helps a bit, good night;)