Polite/professional alternative to 'It turns out'

Solution 1:

I think that if you explain the reason(s) why you cannot do (...) or you don't (...) you can use "as a result".

Perhaps you could start saying "Unfortunately, taking into account that ..., we are sorry to say it is not possible for us to..."

I hope you find my comment useful.

Good luck.

Solution 2:

As it happens...

We have found (alternatively: discovered/realized)...

It seems...

We must (alternatively: regret to) inform you...

The (add one of these if desired: simple/unavoidable/unfortunate) fact is...

Ultimately...

In the end (alternatively: last analysis/long run)...

The upshot (alternatively: result/final determination or verdict) is...