If we start with the sentence:
"This is the first time I've touched a dolphin."
Then the correct way to 'rewrite' the sentence is to remain in the present perfect, ie
1a) This is my first time to have touched a dolphin.
2a) This is my first time having touched a dolphin.
Both sentences are grammatical. I greatly prefer 1a. It's hard to imagine saying 2a.
As for your original "rewrites"
1) This is my first time to touch a dolphin.
2) This is my first time touching a dolphin.
I also greatly prefer 1 here.
And neither 1 nor 2 have to be said at the moment of the touch. For example, if one is on a dolphin-spotting boat as part of an activity that lasts several hours, then either 1 and 2 can be said either before or after the actual touch, as part of talking about the entire experience that has (or is) lasting several hours. In addition, 1a can be said anytime after the actual touch. While, again, 2a seems to me unlikely to be said, and almost as unlikely to be written.
The example sentences, when stated, express "curiosity". It doesn't necessarily mean that it has to be experienced, rather, the speaker ponders on what something (particularly an activity/circumstance/experience) feels like.
Best Answer
This sentence starts off just fine. Verbs that command to someone to do something have the "implied you" as the subject. This is called an imperative sentence. As it says at one website:
That said, the sentence could still be improved; "someplace" is one word, and the second half of the sentence should include the word "will":
This sentence has problems. The main verb here is learned, not observed. You could fix this in one of two ways:
Fix No. 1: Start the sentence with a prepostional phrase
This would require you to change the word "observed" to its gerund form:
Fix No. 2: Start the sentence with the subject and use a conjunction
This could be accomplished by using a compound verb:
or by making it a compound sentence: