The block presented with the second link (api.blockcypher.com/v1/btc/main/blocks/1) is not the same as the one presented with blockchain.info.

"api.blockcypher.com" says block 1 (Height=1) has a "previous block" of all zeroes: but that is the block with Height=0, not with Height=1 !.

One could argue that "api.blockcypher.com" starts counting (oddly) on "1", but the problem is that their next block (block 2) has a "previous block" of "00000000839a8..." (correct) which in fact is not their block 1...

That is, there is a gap in their API, and the block with a "previous block"="000000000019d66..." or block with Height=1, is not accessible using block count:

• "api.blockcypher.com" block 1 is really the block 0 (Height=0), and
• their block 2 is the correct block 2 (Height=2), and so
• the block 1 that you are trying to see is unreachable in that API (!).

That also means that Nonce=2573394689 for block 1 from blockchain.info is the correct value.