Is it possible to make a high availability PostgreSQL database cluster by open source softwares?
With all high-availability solutions you will always have some down-time during a failover, typically less than a minute.

The reason is that the clusterware has to determine reliably that a member is down before it can fail over. That means that failover is only initiated after several attempt to communicate with the cluster member have failed.

You can reduce failover time by making these tests try less often, but that increases the risk of an unnecessary failover (for example, caused by a one-time network glitch). Unnecessary failovers reduce the total uptime of your database, so you don't win anything that way.