The premise of the book was as follows: a scientist creates a time machine and travels to the time of Jesus to see if he's real. Upon arriving, he finds no Jesus. He then decides to be Jesus and follows through with the work of Jesus and is crucified.
That sounds a lot like the rather unlikable book Behold the Man by Michael Moorcock. See Behold the Man (novel), Wikipedia. It's a pretty good match for your description: Time machine, no Jesus, time traveler takes his place and is crucified.
Possibly you are thinking of "The Didymus Contingency" by Jeremy Robinson.
If you could go back in time...and witness any event...where would you go?
When Dr. Tom Greenbaum faces that question after successfully discovering the secret to time travel, he knows the time, place and event he will witness: the death and failed resurrection of Jesus Christ.
The plot seems to be quite similar to this one: https://en.wikipedia.org/wiki/Caballo_de_Troya
The plot of the book unveils the last period in the life of Jesus Christ as revealed through the first-hand experience of two pilots (or rather "timenauts"), members of a US Air Force top-secret military experimental project on time travel codenamed "Operation Trojan Horse", who in 1973 supposedly succeeded in travelling back in time to the land of Palestine in the year 30 A.d.