You can use any Ethereum node, or run your own. MetaMask supports arbitrary RPC servers for this very purpose, so you can use Flashbots, for instance.
This would require more than just a mobile device, however. Perhaps a rooted Android device could self-host an Ethereum node, although your battery life may take a hit.
I think there are other chains and wallets that are designed around mobile use cases, which make it easier than on Ethereum to sync the whole chain, or use technical means to mediate the need to do so.