Installing a third party client is not a long term solution for the recipient. It is only going to cause problems for the recipient in the future when they end up with the exact same problem whereby their messages are not being received yet they're not being notified that the attempt failed. In theory RCS should fall back to SMS if RCS can't be sent but it often doesn't.
In practice I recommend that the sender and recipient turn RCS off (& in this case not install the Google Messages app) since it causes so many problems since almost no one supports it (other than Google). If that's the reason the OP couldn't receive messages then the problem is with the sender. Their client is failing to send the message without notifying them that the message failed to send.
I used to use RCS with Google Messages and turned it off because it wasn't letting me know that messages had failed to send yet weren't being received.
It's the sender's problem, not the recipient's problem. The sender needs to turn RCS off.
If you want instant messaging you're probably better off using iMessage if you're on an iPhone or WhatsApp which is available on Android and iOS. Stick to using SMS and MMS if you're using carrier services.
