jmj lore to my knowledge has inconsistencies but here is what i know!!
so when they first met it was in vocal room. mj was with 3 other trainees when jm walked in, apparently the atmosphere was awkward but jm as sunbae decided to introduce herself first and showed them around. so mj said she thought jm looked unique like a model and was tall while jm said "she really looked so soft and warm like a freshly steamed potato." and she thought she needed to take care of mj.
its cute and all buttt in another interview -around the time of savage- jm said they were this rivalry between them since they started to train around the same time. when they first started to train they were in different groups (jm was with ningning and mj was with chaehyun i think) so maybe thats why their rivalry started! (here is a cute story back when they were in different trainee groups: https://twitter.com/sunshine_080507/status/1604481798746296321) the idea of them hearing stories about each other and learning these little stuff without being friends is so cute to me!!
anyway aespa's line-up changed so much but jm and mj were always in these line-ups so i assume they were put together in the same trainee group at some point (they said they performed keep your head down for one monthly evaluation) and when that happened the rivalry faded i guess?
the reason i said its a bit inconsistent cause im pretty sure jm said they met at dance practice, said mj was cute and a "precious friend she need to take care of." while there is whole other stuff with the vocal room so again i assume it went like: very first meeting at vocal room, after that they werent friends but rivals. then they got put in same group, jm saw mj in dance practice room and her cuteness aggression got trigged, they became friends.
additional notes: they were told they were going to debut together but their recations were tame because at that point they were told countless times already and they started to think they weren't going to debut at all. jm bought mj her first alcohol when she turned 18. when they were taking the bus if they missed the time jm would run after the bus and hit the doors till it stopped and it took them in. they invented the jmj cross during the trainee days. even then jm teased mj about her cheeks.
if you have questions please ask!! sorry if this is so long:(