"I can only imagine... " means: "the only (single) thing that I can think of", or "The only (one/single) thing I can do is guess". By saying "I can only imagine... ", it means that you don't know the answer or you son't know what to say, so you have to guess. It's like starting the sentence by saying "I guess...". For example: Richard doesn't know why Sonia wants to learn English, so he can only imagine (just guess) why she wants to learn English. I'm sure you noticed that I wrote "just guess". The word "just" has 7 different uses. One use of "just" is to say "only". I can just play the guitar = The only instrument I can play is the guitar. I hope this helps...

In this context, "I can only imagine" means that I know I'm going to be amazed by you.

I can only imagine means to speculate about something I can only imagine he is late because the bus hasn't come. I can just imagine is predict something based on something/somebody you know quite well. I can just imagine you going to work with no tie on.