Question

can we use either did or had if the sentence is past when we are changing as soon as to no sooner than and vice versa

Answer 1

yes we can use did or had for past

Answer 2

Yes, you can use did or had if the sentence is past when we are changing as soon as to no sooner than and vice versa.
Example:
As soon as he had received the message he e-mailed to his friend.
No sooner than he did received his message he e-mailed to his friend.