A lot of useful info in the sidebar: https://www.moneroinflation.com/ "We are 9y 114d 11h 20m 29s without an inflation bug" (i.e. since the launch of Monero in 2014) and here: https://sethforprivacy.com/posts/dispelling-monero-fud/#you-cant-audit-the-monero-supply

Block rewards are transparent and can be seen in any block explorer such as https://xmrchain.net

Nodes verify the supply via cryptographic range-proofs, meaning that it can be mathematically proven for every transaction that inputs - outputs = 0, without publicly revealing the exact amounts (only the sender and recipient can decrypt the encrypted amounts).