"Proof that Marcion existed" is a bit strong (and a bit circular, too, actually -- which the arguments based on "the criterion of embarrassment" usually are), but there is a plausible connection between the Acts 16 passage and the Marcionite phenomenon. Joseph Tyson in
Marcion and Luke-Acts writes:
A plausible suggestion is that in the second century Bithynia, which was generally connected with Pontus, was known as the place of Marcion’s origin and that Luke wants to disassociate Paul from Marcion. He does so by affirming that in the very area where Marcion was born and began his preaching, there had been no Pauline mission, thus no association with earlier Christianity. The author of Acts would be signaling the reader that the claims of the Marcionites to be followers of Paul are mere fabrications, unsupported by the historical “facts” and, what is more important, contrary to the “Spirit ofJesus.” (p.77)
The suggestion is only supported, however, by the larger context (and details) of Tyson's argument that the canonical form Luke-Acts is an anti-Marcionite redaction.
(What I find of particular interest is that Paul turns instead to go to Troas (the region of Troy) where he receives a vision that leads him to a new continent and a place explicitly said to be a "Roman colony". This is one of numerous shadowy echoes of the myth of Aeneas and hints that the author had that myth in mind when he narrated the preparation for the church's base being moved from Jerusalem to Rome.)