In BGP, we have two AS (100 and 200) and we have announce IP’s with network command in both AS so can its are ping each one without IGP
There has to be some kind of connectivity or reachability among BGP peers.
In the picture, two BGP peers share the same subnet on one interface (AS100, AS200) therefore there is reachability and TCP connection will be successful, This example does not require a route to the BGP peer. Now consider Router 3 will need a route that points to Router1(AS200) in order to make a BGP connection, so Router2 AS201 will have to either redistribute connected or share a default route to Router 3 so they can form neighborship.
Hope this helps
Consider IGP only in I-BGP and not EBGP. EBGP neighbors should have same subnet or ability to talk to each other by some mechanism.