Harder to think- or solve problems while talking to colleagues. (Introverted)

I work as a software developer and sometimes I’m in group projects. One thing I hate is when I have to come up with suggestions or solutions while being in a group meeting or talking to a colleague. I just feel stressed and pressured. I prefer to sit on my own, go through the different scenarios and cases inside my own head methodically before opening my mouth. Because how am I supposed to come up with a good solution if I don’t get time to think it through first, right? I don’t even get how they do it or of they just take the first solution that enters their mind.

But saying “Sorry, but I need to think about yhis on my own first.” in a meeting might come off as rude, arrogant or plain weird. I think this has to do with my introverted and calm personality.

Can any relate? How do you deal with it?