That is a bit annoying, but I think it's why the carrier types are easy to swap - you should be able to fit it without a base, using the seatbelt? Most infant carrier seats you can. TBH, under 6 weeks some newborns struggle to get a good fit even in an infant carrier, so it is very early to get a good fit in a multi stage seat. (Not a blanket rule - some seats are better than others at this).
It's possible he'll get a better fit in the 360 seat by about 3-4 months, once he is better at supporting his own head, but if it's very tilted upright because of the shape of the seats in your car/position of the isofix points, then you might need to wait until he's sitting up with less support. The infant insert stays in until 75cm which is car seat industry shorthand for about 9 months and/or ability to sit unaided.
If the back seats in your partner's car are flatter, or the isofix points are higher up compared to the sort of corner of the vehicle seat (if that makes sense), the Enfasafe seat might get a better fit there. If you choose a different seat for your car, find a shop you can try it out before you buy to make sure it's not too upright - it can be a problem if you have the combo of isofix points right down at the very bottom of the backrest plus tilted back angle of the seats.
Check that the support leg isn't overextended as well. If it's set too long, then the seat will be tilted further back. The child seat should rest on the edge of the vehicle seat, where an adult's knees would go. If you can push your hand under there at that edge of the seat, try shortening the leg and see if it improves the angle.