Well, first off, the claim is not increasing violence towards trans people it's just there exists violence towards trans people and framing the debate as "let's talk about whether you exist" does little to help that.

As for sources, hard stats can be difficult for any hate crime (compounded by the fact homicide against trans individuals isn't often recorded as violence against their actual gender) and especially considering that the total trans population is small (and thus vulnerable to effects of small numbers) but the FBI hate crime database [0] and the NCAVP reports [1] are good places to start. Transequality center also collects good resources.

Somehow, I don't believe you've really wondered about this too much...

[0] https://ucr.fbi.gov/hate-crime/2017/tables/table-1.xls

[1] https://avp.org/resources/reports/

[2]https://transequality.org/issues/anti-violence