Unfortunately, most life will likely be Carbon based, in some manner (synthetic life could be different). The key is forming the large, complex molecules that make life, life. You need an element that can form chains. You also need to attach things to those chains.

The only 2 atoms that can do this are carbon and silicon. Both can form "organic" type molecules. Unfortunately, silicon has an additional reaction pathway that makes the chain easily break down in the presence of water. The conditions for silicon based life are so odd as to be unlikely to happen on the scale needed by natural processes. There might be some work arounds we don't know about, they would be extremes.

Synthetic life is another story. Once you have active control over your environment, a number of other options open up. The first step is the kicker however, getting from abiotic natural rubble to a working replicator.

There's a reason we are looking in Goldilocks zones, they are the most likely environment for the only process that seems viable.