How would I go about exploring Bitcoin's entire block chain? I'm trying to wrap my head around bitcoin/blockchain and from what I understand, every transaction that has taken place in bitcoin is placed into a block and after this block is validated it is added to the block chain in chronological order.  

Is there some place that I could go to look at the first block of transactions for bitcoin?  Or any random block of transactions?  

If anything I have said above indicates that I have misunderstood some part of the process - please don't hesitate to correct me.
The easiest way to look at the transactions in any arbitrary block would be with a block explorer. 

As of the instant I'm answering this question, the newest block is block #456238, so you can peek at any block by creating an address for a web block explorer as follows (Blockchain.info for illustrative purposes):

https://blockchain.info/block-height/0

https://blockchain.info/block-height/456238