Is there solution for event where nobody would mine some coin?
The original software wouldn't even mine if it didn't have other peers. And there is a large gap in time between the release announcement of bitcoin and block 1 being mined, so I think it's doubtful that Satoshi was alone at any point except maybe during the period when the network wasn't even making one block per ten minutes.
'other peers' is in regard to X operations of software, not people
satoshi running X computers means satoshi could have been alone before hal then joined many blocks later(block 78)
also solo mining in those days did not need multiple computers to hash a block ID for a single block candidate..
also the reason why the first 77 blocks took (as timestamped) 2 days to accomplish can be explained by many things(common sense)
a. using the timestamp as a nonce means we cant truly trust that it actually was 2 days
b. he stopped and started his software for many other reasons(sleep, updates, bugs)