I understand that the server will send its SSH version and the client will do the same. What I am wonder is if the order matters.
Additionally, I'm wondering if I could make an SSH server receive an SSH version from a client before sending its own version?
The order of the SSH protocol version exchange is unspecified; it says:
When the connection has been established, both sides MUST send an identification string. This identification string MUST be
SSH-protoversion-softwareversion SP comments CR LF
The RFC is likely silent on the protocol version exchange order because, practically speaking, it's a race and the order should not matter. When the client's TCP connect is accepted by the server, the client and server send their version information...who gets to the other first is just a matter of speed, traffic, etc.
As a client, you cannot (or should not be able to...) "make" the server wait; it's certainly possible that a particular server implementation waits for client before sending its own information but that's a server implementation detail.