Is Special Research the only way to obtain Mew?

While there hasn't been anything officially announced on the subject, it is safe to say that the current line of Special Research - "A Mythical Discovery" is the only way to obtain Mew.

For inference:

• Mew is not an EX-Raid boss.
• Unlike Unown, who appears in the wild very rarely, Mew absolutely does not spawn.
• Mew has not been encountered in any conceivable fashion before this release - wild spawns as mentioned or raid battles.
• Legendary and rare/desirable Pokemon have been withheld for release despite their existence in the actual game code for special events before - notably, the Legendary Raids can still accommodate Articuno to this day, but at the time of writing, it hasn't been in a raid since its first rotation.