Hello @Pablo_Letellier, welcome to the community!
You don’t have to pay for the first month in order to transfer the site to your client. This depends on what type of Workspace you have with Webflow, but typically if you are transferring a site to a client, the client has to pay for hosting on his/her own Workspace. Alternatively you could keep the site on your Workspace and use, the newly restored, Client Billing feature to charge your client for hosting directly. Now the best way to work with clients without worrying about this transferring and billing issues, is to request access to your client’s Workspace, that way you can just access their Workspace and do your work and they will take care of the rest. I hope this helps!