1: This is the first time I have ever done something that I am still doing1
2: That was the first time I had ever done something (no 'still doing' implications)
You can't really usestart #1 with thatThat is..., in #1, but you could usestart #2 with thisThis was... in #2 - so long as someif preceding text has established the sushi-eating occasion as a "current narrative topic / focus".
Equally, you can't use the combination of verb tenses This is ... I had in #1, but you could use That was ... I have in #2. The second verb form is really just a stylistic choice reflecting whether the speaker is more interested in talking about his past or present circumstances.
1 Sometimes you might use Present Perfect like this if you've very recently finished doing something. For example, you might say #1 to the maitre d' as you leave a restaurant, after having eaten sushi there. As ever, Present Perfect simply implies a very strong connection to "time of utterance", so that scenario is "close enough".