She could not go to the party as she did not have an invitation.
As she did not have an invitation, she could not go to the party.
What is the difference between them?
There is a change in emphasis, but no change in overall meaning. 1 empathizes her not going to the party, with the lack of an invitation being merely the reason, while 2 emphasizes the lack of invitation, with not going to the party being merely a consequence. Depending on what esle is being written, and the intent, one or the othr might fit better, but they could be interchanged fairly freely.