You are wrong.
You are misunderstanding how bitcoin works.
BTC are assigned by a miner to himself using a transaction. When the miner is building the block, he includes a special transaction (commonly called the "coinbase" transaction or the "generation" transaction) in the block that pays new bitcoins to himself. He can include additional transactions in the block if he wants to (and will gain the transaction fees from those transactions which chooses to include), but he is not required to do so. The only transaction that is required is the transaction that pays the miner his block reward.
So, in the beginning Satoshi created a transaction that paid himself 50 BTC. Then he built a block from that transaction. Then he completed the proof-of-work on that block. No chicken or egg problem there.