Can a node broadcast a valid signed raw transaction while still syncing? Built and signed a native bech32 UTXO, but when I attempt to broadcast from my testnet node using the command sendrawtransaction it returns "missing inputs". I don't have the private keys in my wallet, and the testnet node is still syncing, but I was able to broadcast it fine with a testnet API service that lets you broadcast signed transactions. 

Is it possible to broadcast a raw signed transaction to the network while still syncing?
You can only broadcast transactions if your node has synced to the point that it knows the outputs that were spent. This is because your node will always validate a transaction before it broadcasts it. If it has not synced to the point that it knows the outputs that your transaction spent, then it won't have the information necessary in order to validate the transaction.

So if your transaction spends outputs that were recently confirmed, then you will have to wait until it is basically fully synced before you can broadcast. But if your transaction spends very old outputs that are deep in the blockchain, then you can broadcast before it has synced.