There will be a hole. But if you are talking about the one in Pewter City, then you must defeat Brock first, in the Gym, so you can get your The Boulder Badge. You will have to defeat Geodude and Onix though, which i recommend to not use Electric pokemons in battle.
You can find the Cerulean Cave in the northwest corner of Cerulean City in Kanto in Pokemon LeafGreen. The cave contains the Pokemon Mewtwo.
There is no awakening cave.
Diglett cave
in cerulean cave.
How to get to lost cave in leaf green??
that would depend on which cave, for there are many caves in leafgreen.
Altering cave is on 5 or 6 island.
There not in cerulean cave.
Cerulean cave
back of cerulean cave
on four island
its on 4 iland