Can ordinal numbers be used with the indefinite article?
For example, "We've seen robots, but we haven't seen dancing robots. This is a first."
If they can, in what cases?
Having given your question and the first response some further thought, here's a second.
I wrote the above as an example of how indefinite article + second could also work. It works, because I want to imply that there might be other second responses. Mine might be only one of several. If I'd wanted to suggest that mine would be the only second response, or that it was important to distinguish between the second response and the third, then I might have said, "Here is the second." ("The first response" works, because there is only one.)
When someone says that something is a first, there is an implication that there is a list of "firsts" out there somewhere that has now been added to. Some people actually keep lists of firsts. (Do an Internet search of Pennsylvania Firsts, for example.)
When someone says that something is the first, the implication is more that there will be (or have been) others in the same category or sequence (a second, a third, a fourth, etc.), but that this one is the first.
So, thinking about your and Paul's examples, the contrasts might be something like this:
"We've seen robots, but we haven't seen dancing robots. This is a first."
"India sends a rocket to Mars: this is a first."
They are both first times and could be added to a list of "firsts". They are not the only "firsts"; there are other "firsts" of other kinds.
"We've seen robots, but we haven't seen dancing robots. This is the first."
This is the first time that we have seen dancing robots, but it implies that there may also be a second time for us later, or that it might not be the first time for others.
"India sends a rocket to Mars: this is the first."
This is the first rocket that India is sending to Mars. There is an implied suggestion or expectation that more (a second, a third, etc.) will follow.
And to further complicate things for speakers of languages that don't use articles, there are times when we might choose between the, a, or no article.
He received a first prize in the competition.
(What kind of prize? A first prize.)
He received the first prize in the competition.
(Which prize? The first prize.)
He received first prize in the competition.
(What did he receive? First prize (here it's like the name of the thing that he received))
Notice that I used a + ordinal number several times. I think each use fits the pattern that a + ordinal is answering the question "What kind of place in the sequence of events is it? Is it a first, a second place, a third place, etc.?" And the + ordinal answers the question "Which particular place in a particular sequence is it? Is it the first place, the second, the third, etc."