When my friend started playing valorant he had this problem too. It turned out that Valorant really dislikes HDD. So if possible, try to switch to SSD.
If you can't change the disk, there are a couple of options.
*Free up as much disk space as possible.
*Defragment the disk
*Run 1-2 deathmatch (not a team one) before your favorite other mode, the system caches repeated requests and subsequent loads will be almost instantaneous. Default deathmatch does not give any offences, so after the end of loading you can immediately quit and start the next one.