Look up "Lightning Network". This is a solved problem. You can build on top of bitcoin to scale basically as large as you want, trustlessly. The software is being developed as we speak.
https://medium.com/@jonaldfyookball/mathematical-proof-that-...
This is unsupported. LN is a research project, not a production-ready payment system. It has plenty of limitations (trustlessness is a huge limitation), and the topology of the network doesn’t match that of a real economy (routes to fellow consumers are practically useless, since everyone wants to pay merchants). There’s plenty of work left before LN can scale properly, if it ever manages to (again, trustlessness for both senders and receivers is setting the bar as high as it can possibly go).
Scalability is secondondary for LN, trustlessness is primary. Due to this choice I predict difficulty in scaling sufficiently.
Also, everything is done via two-way payment channels in LN, which means that you need to lock X BTC in a channel in order to send it, which becomes very capital intensive for nodes close to merchants who need to lock millions of dollars worth of bitcoins to cover merchants’ monthly turnover (this is in addition to the BTC locked up by other nodes who participate in the transfer but are not directly connected to merchants). If you want to send 0.1 BTC through 10 nodes, each of these 10 nodes must have locked up 0.1 BTC on the blockchain, and you’ll pay blockchain fees if just a single channel/node in your path doesn’t have at least as much as you need to send.
A proper payment network needs two different types of nodes: senders and receivers. Using a single type of node for both doesn’t make much sense, since merchants and consumers have completely different needs. Senders need to be able to send relatively small amounts relatively frequently (a consumer making a few purchases per day), while receivers (merchants) need to redeem relatively large amounts (e.g. one week’s worth of payments) relatively rarely for bitcoins (on the blockchain).