First of all, this is an observation by Luke who was not an apostle but a recorder. All recorders record things as they see it. The fact that some received while others Refused made no sense to Luke (nor to me) and so he could only assume that some were ordained and others not.

So, which comes first, the believing or the ordaining?

This verse makes it sound like the ordaining came first. However, if one is ordained to eternal life then believing is unnecessary. This cannot be.

When a person believes on Christ Jesus, they are ordained to EternalLife. Joh 3:15 1Jn 5:11

Always remember that the Lord sees the end from the beginning. He knows who will receive Christ Jesus but He does not force or deny anyone access to His Grace.