Can anyone help me here? I'm really concerned at the moment and this is urgent

So I got an offer from a company in the UK. I'm currently under Tier 4 Student Visa but I'm only here for a short term course.So that means I don't have any UK degree and I can't switch from Tier 4 to Tier 2 directly. I need to go back to my home country and apply there.
Therefore, from my understanding, my company needs to apply for a restricted COS for me and it already has sponsorship license. The procedure of doing so is first to do the Resident Labour Market Test (RLMT) and then apply.
But many people have told me that it is impossible to pass the test for a graduate role as there are so many graduates here in EU. But when I called several agencies, some said for my salary(over £30K), it's not an issue to pass the RLMT.
So can someone answer my questions please? Is it possible to pass the test for a graduate IT role? Is it difficult to get a restricted COS? Do you guys think if my company is willing to help me? (I mean sounds to me the procedure is quite complicated.)
I have already got the offer and I'm waiting for my contract. Should I sign the contract without knowing if I can get their sponsorship first?
Please heeeeeeelp!

Many thanks!
Lucy