Stroller suitable for small baby?

[LittlePeachh]

Looking for any advice or recommendations.
We've been stupid had an oversight. I'm a new driver and we chose a car that is on the smaller side, but still has space for 2 kids (just). The only thing is the boot isn't large.

Our pram doesn't fit in the car whatsoever.
I need something that will be suitable for a 6 week old to go shopping, taking DC1 to preschool and hobbies.

I've saw 2 strollers that parent face but have larger wheels, unsure if they'll fit (My Babiie MB50 or Puggle 2in1)
Looking at compact strollers that have a mesh back to see baby fully, but this takes away the ability to see baby, interact etc which I feel is necessary... it's of course only for an hour or so max?

Can anyone give advice or recommendations please 🤞🏼
TIA.

Look at baby jogger Citi minis, they world face but fold small. Or maclaren techno xt- an oldie but a goodie. Any stroller that lies flat will be ok for babe.

@FantasticMissFox thanks for your reply, I will have a look at them!
I have seen a couple at lie flat, hopefully can go into a store and scope some out to get an idea of what I'm looking for.

YoYo with the newborn pack, not the bassinet.

Or do you also need the stroller to work for the eldest? Uppababy cruz with the snug seat insert for the baby could also be a good choice if you need both to use it and it can comfortably take a buggy board if that also appeals (the YoYo has one but it isn’t easy to push).