Ah, you never forget your first time!
I think it's more natural to say, "This is the first time I've come to ..." (or I've attended ..."
Regarding the second example
This is our first time to meet, Amy
this is quite awkward. The comma after meet tells me you are speaking to Amy, telling her that (despite her sense of deja vu*) you've never laid eyes on her before.
To say this, I would use
This is the first time we've met, Amy
On the other hand, without a comma after meet, you are saying it's the first time you've met Amy and you are saying it to someone else. Maybe Amy's husband has just accused you of seeing his wife frequently. Then you would say, instead:
This is the first time I've met Amy. Honest! Please put down that gun!
*deja vu = an eerie sense that one has been somewhere or done something before, when it probably is not true.
Student or Learner