By uttering this objection, your friend has given you evidence of their ignorance of history. The Bible (specifically the New Testament) is by far the most well attested set of documents from antiquity. Even the most liberal scholars estimate that the latest book (the Gospel of John) was completed by the end of the 1st century – well within the possible lifespan of the disciple. Claiming that there isn’t a shred of evidence for Jesus’ existence flies in the face of the vast majority of scholarship in the area – no serious scholar has made that claim for decades.
The New Testament documents are unreliable because they were recorded at a much later date.
The New Testament documents cannot teach us anything factual because they are a religious text (this is a likely assumption although it isn’t implied by the objection).
There is no objective (non-Christian) evidence for the existence of Jesus.
My approach with someone who is hopelessly off base is to ask them about their sources, but I’ll generally frame it by saying “Oh, that’s an interesting point – how did you come to that conclusion?” From there I will ask them how their theory handles some of the following facts:
We have fragments of manuscripts of the New Testament that date back to the middle of the first century.
Church leaders in the early second century quoted scripture liberally and used the same passages (a hard feat to accomplish if the passages in question weren’t in existence for another 100 years or so).
There are no historical sources before the late 18th century that claim Jesus was not a real person – most importantly no contemporary opponents of the early church ever claimed that Jesus’ existence was mythological.
There are at least 10 non-Christian sources from the first and second century that either mention or imply Christ’s existence AND resurrection!
New Testament Authors were not writing mythology but history. (Whether or not you agree with their content is a different issue – they intended to relay factual accounts c.f. Luke 1:1-4)
Instead of rattling off all of these statements, I find it's best just to ask “Our theories are supposed to explain facts, so how does your theory make sense of _______?”
If it seems like they are going to dig in their heels, don’t feel the need to try to prove something to them. They are in the vast minority both historically and scholastically and therefore the burden of proof rests on them. If they are open and have not considered these things, you can segue into a more meaningful dialogue by acknowledging how much misinformation exists on both sides as a result of wishful thinking instead of historical research. Offer to look into it together and try to begin with whether or not the New Testament is an accurate representation of what the earliest Christians believed (it is); if they come to this conclusion you can suggest reading the earliest Gospel together (Mark) and viola – you’re in a GIG!