I think that I would try to argue that we can know God in two ways, and that both are His revelation.
First, I would agree with the agnostic to a certain extent. I would say that if all we have to go on is our own knowledge and perception, then we would not be able to know anything beyond the natural world that we can sense and interact with.
I would then try to have them agree that, in theory, it is possible that a supernatural being could, if it so chose, give its creation a way of knowing it. The issue then would be not that it’s just impossible, period, to know God or anything about Him, but simply a disagreement on whether in our current situation we can.
Finally, I would present the facts as Catholics understand them. That God has indeed chosen to reveal Himself to us. First, we have His Word, holy Scripture, which has captured the events of history, revelations from God and angels, and the messages of His prophets. I would also present the Catholic view that, through reason alone, we can come to see God and understand something about Him by examining His creation, The universe itself points to God.
At this point, the agnostic will likely disagree that either of these things “prove” God. However, I think that if you take the conversation to this point, you can now start discussing specifics. If they think that the Bible is just a collection of myths with no basis in historical truths and no different from any other religion’s books or the myths of antiquity, we can begin an apologetic work to expose why that’s false. If they don’t see how nature points to God, we can explain that as well.
I just think that such a viewpoint really comes from not actually examining the evidence before us. It seems nonsensical to believe that we can’t know anything about God. There’s a lot of assumptions implicit in that statement; for example, we can’t know anything about God because He hasn’t told us anything about Himself, or if He has we can’t know it. As Catholics, we have evidence to the contrary of both those assumptions. So, we just have to move the conversation along to get to those unstated assumptions, and answer them.
It may also be worthwhile at some point to address what proving God means. They may have some vague idea that this proof of God would be overwhelming and irrefutable. No person alive could argue with it, it wouldn’t have to discussed or wrestled with, it would simply be manifestly true! However, there are people today who don’t believe that the world is a globe. There is no truth so true that people can’t choose to deny it.