I downloaded the app and sent my coins to the address but I noticed this app is syncing, which can take a long time. So I tried to put myself in a casual user's perspective. Does the person trying to rent space have to also wait for the program to finish synching? And if yes, then I wish they had a way around this so that those people don't have to wait around for the sync to complete.
Yes, you need to wait the blockchain to sync or otherwise the siacoins you transfer for renting storage space will not show up in your balance.
And yes, there is a way around: try with a manual download, AKA bootstrapping
https://siawiki.tech/daemon/bootstrapping_the_blockchain