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While the cave is technically "open", it will be blocked by an NPC once you awaken Rayquaza. I've found the type 3 level script at offset 1E56EF in Sootopolis city using Advance Map.
Here is the script:
'---------------
#org @start
setflag 0x87D
compare 0x405E 0x1
if 0x1 call @snippet1
compare 0x40CA 0x1
if 0x1 call @snippet1
call @snippet2
call @snippet3
compare 0x405E 0x1
if 0x1 call @snippet4
compare 0x405E 0x2
if 0x1 call @snippet4
compare 0x405E 0x3
if 0x1 call @snippet4
compare 0x405E 0x4
if 0x1 call @snippet4
compare 0x405E 0x5
if 0x1 call @snippet4
compare 0x405E 0x2
if 0x1 call @snippet5
compare 0x405E 0x3
if 0x1 call @snippet5
compare 0x405E 0x4
if 0x1 call @snippet6
compare 0x405E 0x5
if 0x1 call @snippet7
compare 0x405E 0x6
if 0x1 call @snippet8
end
The NPC that is blocking the cave entrance has the person event number 1 in Advance map and I'm pretty sure that this part of the script makes it stay near the entrance:
#org @snippet8
movesprite2 0x1 0x1F 0x12
return
So you could try modifying the 0x1f to some other value like 0x1e so the NPC is no longer blocking the cave.