Hey
@Ste_Vege, good news, I called a friend and asked them about your question. I mixed a couple things before, sorry for that.
CSQ is not needed for open work permit in your case. Told you I didn't know enough about sponsorship haha
Here it is more information
"Once they receive their acknowledgement of receipt letter, they can apply for an open work permit. They must apply online. "
https://www.ircc.canada.ca/english/helpcentre/answer.asp?qnum=1163&top=17
Cheers and good luck, hope you can become PR soon.