A google search tells that Shiva Gita is a conversation between Lord Shiva and Lord Rama. It is from Uttarakhanda of Padma Purana.
Which chapter of Uttarakhanda is Shiva Gita found?
Who was the first ever to refer to Shiva Gita? In which century?
I don't know which version or edition of Padma Purana has this composition of Shiva Gita. It also looks like none of the acharyas before 15th century have written any commentary on this text.
The only reference to any kind of a timeline I have seen is only here. Sri Abhinava Nrisimha Bharati (1600 – 1623) of Sringeri Sharada Peetham, seems to have written a commentary on Shiva Gita.
An expert in mantrasastra, Sri Abhinava Nrisimha Bharati was an adept of a high order. A commentary on the Shiva Gita, that he wrote, is an outstanding work.
The only available translation of this text I have seen online was by a Santosh Kumar Ayalasomayajulu, initially found here. Curiously, that book has now been removed, which is odd. But regardless, there is no need to consider that as a loss, because even in that text, there was no actual reference to the parent text it was derived from (apart from simply saying uttara khanda of padma purana). And it also doesn't mention which acharya's commentary his translation is based on. So, I am not inclined to take it as an authoritative version. Curiously, the same translated text is also found here.
You may also look at this question on this very site. It looks like not much material is available on or about that text.
Even though the Shiva Gita is not to be found in the various extant editions of the Padma Purana, this chapter of the Narada Puranam summarizes the content of the Padma Puranam and says the Shiva Gita is part of it:
देवरातसुताख्यानं पुराणज्ञप्रशंसनम् ।। गौतमाख्यानकं चैव शिवगीता ततः स्मृता ।। २५ ।। https://sa.wikisource.org/s/507
This way one can be assured of the authenticity of the Shiva Gita which has several commentaries.