Having a block explorer doesn't really change much about the level of privacy that bitcoin offers. Not to mention that before 2010 there weren't that many transactions to go through anyway, you can even check all of them manually if you skip the coinbase transactions since there are only a little higher than 200 of them in first year: https://blockchair.com/bitcoin/transactions?s=time(asc)&q=time(2009-01-03..2010-01-01),is_coinbase(false)#f=block_id,time,is_coinbase