Yep I've got a software wallet and a hardware wallet that I'll be transferring it too, when I do I'll be able to see that TX on the blockchain, I understand that, but I was expecting to see a blockchain transaction for the initial purchase from Binance. Is that a case of because its not specifically my wallet and its on the exchange, I won't be able to validate the purchase on the blockchain?
As far as I know, when you are buying BTC using FIAT, it is most likely that Binance used an "
Internal Transfer or Off-Chain Transaction" which means that transaction ID that has given to you cannot be viewed on the blockchain explorer. This event is similar when two people makes a transaction using only their Binance account. Like for example, when User A sends some bitcoin to User B considering that they are both using Binance platform to send their coins back and forth. Note that internal transfer does not charge you with tx fees.
On the other hand, you can only view your txID to an explorer when you withdraw your bitcoins to your hardware wallet or software wallet, this is called "On-chain transaction" where you will paying tx fees and it is not instant (this is the normal transaction happening in bitcoin space).
[1]
https://www.binance.com/in/support/articles/360037409611[2]
https://en.bitcoin.it/wiki/Off-Chain_Transactions