Curling and maybe rowing.
I couldn't find anything official, and I didn't understand all the information I found on rowing.
I went down the list of Olympic sports and made my own list of sports that seemed to involve team competition. Most are pretty obvious, but several I wasn't certain of. Sailing in particular appears to only have events with one or two sailors at a time, so not a team event for this question.
- athletics (some track relay events are teams. Not sure of any others
- cycling (team pursuit)
- gymnastics artistic
- gymnastics rythmic
- swimming (some relay events are team competition)
- synchronized swimming
- water polo
- ice hockey
As this is my own list, there could be mistakes. Many of the major sports I know (like team USA basketball and ice hockey) have a national team that is composed of selected individuals. For the others, I tried to find information on the selection process.
The only ones that seemed likely to be similar to curling to me were bobsleigh and rowing.
Everything I could find for bobsleigh suggests that individuals are selected onto the national team. I don't know how the competing teams are put together, but it appears to be after team selection, not before.
The last one that bugged me is rowing. There seem to be different procedures for selection by different rowing classes. So while some individuals are chosen, I got the impression that some classes might be selected as a crew through trials. If anyone knows more detail about rowing to rule it in or out, that would be appreciated.