I'm not aware of any rule that says we can't. It virtually never happens, because the league has a system whereby all clubs can request another club that they won't clash with, and if both clubs request not to clash with each other, like Liverpool-Everton or Burnley-Blackburn, then their league...
I suspect they would prefer to wait until after the transfer window closes. If we have to play 4 home games without our full squad, it could be a significant disadvantage.
Mind you, a newly promoted side isn't where you want to play on their first home game. They'll be well up for it.
As for...