The possibility we are alone is just as likely as if were not alone if you sit for a moment and think about it.

1 Universe is infinite and a conservative estimate is around some 14 billion years ago the first stars estimated maybe as early as half a billion years after big bang possibly even earlier than that.

2 If we discard ideas of space borne life or some other exotic lifeform and stick with stars and planets for the development of advanced life and advanced civilisation we find countless chances and plenty of time for it to occur.

3 Given this large amount of time said life should be able to move to new solar system within few thousand generation or maybe less the entire galaxy can be populated on a cosmic scale relatively quickly.

4 First problem why is our galaxy not populated so best explanation is we are alone in our galaxy at the least.

5 Ideas of noble aliens avoiding contact with lesser species are unfulfilling as every advanced species in the galaxy would have to agree on this point this seems highly unlikely.

6 There may be physical limits to expansion but given enough time at least one race should overcome it resulting in galactic colonisation again has not happened.