Is there a way to assign it at the
_hottier nodes at the beginning? When I create the index test-00001 it is distributed over all the nodes.
As you're not using data streams, the new test-* indices will get allocated to the content tier, the nodes configured with the data_content role - which in your configuration are all the nodes in your cluster.
You could configure only the data_hot node to also contain the data_content node role.
Or to opt out of the default tier-based allocation you can explicitly set index.routing.allocation.include._tier_preference: data_hot in your index template.