My understanding of SegWit is that any non-segwit (legacy) nodes will see a SegWit output as an output anyone can spend (i.e. no signature required). This is currently fine since if the miner mines a block with a transaction that tries (illegally) to spend from that output, it will be rejected by the majority of the nodes because most nodes support segwit and see that there is no witness proof as part of the transaction. But my question is how could a segwit output possibly be used in the beginning when segwit was just launched and the majority of the network where non-segwit? Then anyone could just spend the segwit outputs? Thanks!
Segwit was activated using bip9. The precondition for segwit's activation was that 95% of the hashrate was signaling readiness to enforce segwit's rules. Also, a majority of the other nodes had upgraded at that point. Quickly after activation, almost 100% of the hashrate was running a segwit-compatible version.