To start a bank you need sufficient capital
If you have that, you can start a bank, as plain and simple as it gets. This is certainly not about "no one is allowed to start a bank". Apart from that, I don't see what it has to do with your point. Further, it is not my idea that big corporations can and do establish their own "pet" banks (I have provided you a link). In fact, many international or just large enough companies which started as pure production (or whatever) firms are now part of large financial groups which include banks to serve the interests of these groups. The fact that Facebook doesn't have a bank means that it is not a corporation (which it is not) or it doesn't need a bank, just as simple. I don't understand why you continue this futile argument
Gazprombank was founded in 1990. Its not a new bank. Russia being one of the few countries not run by international bankers, it is probably one of the few countries which would allow someone to start a relatively new bank.
Can you name a bank that was recently founded by a large corporation as you claim?
Can you name a large corporation founded recently?
Until you can your whole question is pointless. Just in case, Facebook is not a corporation. On the other hand, Samsung is such corporation (just the first name which came to my mind), simply and unpretentiously called Samsung Group (and it is from Korea). Unsurprisingly, this group also includes quite a few affiliated businesses or owned companies busy with financial and banking operations. As
per Wikipedia, "Samsung Life Insurance currently holds a 7.4% stake in the South Korean banking company DGB Financial Group, making it the largest shareholder". And this is only what can be called public knowedge, something which you can read about in Internet