"I have been there first time": Does this sentence sound awkward?

I have been there first time.

The reason why I think this might not be natural is that the expression "first time" seems to describe "past". You do not use the present perfect with an adverb indicating "past", in my understanding.

However, I feel the phrase below is not that funny.

This is the first time that I have been there.

I am wondering about the relationship between "the first time" and "I have been there". "That" could behave like a relative adverb. If that is the case, the antecedent of "that"—"the first time"—is shared with the following clause: "I have been there". Then, is it OK to say "I have been there first time"?

By the way, Google searches for "I have been there first time" and I have been there the first time" in the UK domain show just 33 hits for the first phrase and 10 hits for the second.

The correct form in American English usage would be as follows:

"This is the first time I have been here," or, "That was the first time I had been there."

Let's say I enter your offices for the first time and tell you how nice they are. You might ask, "Is this the first time you have been here?" And I would answer, "Yes, this is the first time I have been here!" The next day, I mention to a friend that I had visited your offices and admired them very much. I would continue by saying, "That was the first time I had been there!"

Note the use of "that" after "time" is considered optional in both examples. I have left them out in order to highlight the words that actually change the meaning of the sentences; however, including them would not be incorrect.

The first issue is that the correct form of the adverb phrase would be "the first time" or "for the first time", never just "first time".

Examples:

• When I was there the first time, it was different.
• I am here today for the first time.
• I will go there for the first time tomorrow.

As you can see, it's not limited to describing the past. But, as you point out in your comment, there is a second problem, which is using it specifically with the present perfect tense: "I have been there for the first time". This is not grammatically wrong, but it's rarely used because, on its own, it is semantically weird. Without further qualification, it is the same as saying, "among my visits there, one of them was the first" which is a truism: if you've been there at all, then obviously you have been there for the first time. This is an issue about the slipperiness of the English present perfect rather than the adverb phrase itself. For a transient, closed event (which "the first time" usually implies) you don't use the present perfect (whereas you might well say, "I was there for the first time on Thursday").

That said, I'm sure it's possible, at a stretch of credulity, to construct a situation in which "I have been there for the first time" fits.