Sorry OP, it does suck when you are tasked with organizing these things and people don’t help, just tell you how miserable it will be.
I have a new team, most have started during the past 5 months, all are virtual, and it’s been a shit year. I have to find a way for them to get to know each other and hopefully start lifting the black cloud a little.
I know you don’t have a budget, so my plan won’t be totally usable, but here’s what I’ve come up with. I typically buy small gifts and do a lunch plus a dirty Santa swap. This year I don’t think that would work with the new team members. So instead I’m doing this.
I’m coming up with a short survey of truly random questions that don’t provide any insight to the person. (What color is your kitchen? If you were a tree what kind would you be?...that sort of thing).
Then, once everyone has anonymously answered, I’ll send the responses with pictures of the gifts, then the team will match the equally random gifts, with the random answers, and give a short blurb on why they chose the gift for the answers.
During the ‘lunch/meeting’ I will announce the person, present, and best why answer maybe in a video, and then send out the gifts.
So, yeah people are stuck going to a video call, but they’ll get a small funny gift and don’t have to put much effort into it. Hopefully they will learn a little about their new teammates and have a funny ‘here’s what happened at work today’ story.
Good luck!