What happens when the bitcoin or any altcoin initially launched?
The client will try to exchange blocks and transactions with other clients.
The developer will just have a genesis block created, no-one to sync up at this time, how does the system accept that this one block is the complete state of the blockchain?
Well, in fact your client doesn't regard a bare Genesis block as a complete blockchain - it says "out of sync" which means that part of the chain is missing.
Do we need to have certain number of computers running with the same genesis block to confirm each other that no other blockchain is in the network?
No, not really. Every client developer knows which Genesis block is the right Genesis block and this right Genesis block is hardcoded into all clients. No confirmations or anything are neccessary - everybody knows which Genesis block is right and which Genesis block is wrong. If someone comes up with a different Genesis block, they can build their own blockchain and their own network on top of it but a normal Bitcoin client will ignore that.