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Definitely you can do this with Pulumi, and it’s fairly common to do so. 

For doing this in front of Fargate, you most likely want to create a LoadBalancer in front of the Fargate Service and attach the LB to your domain. 

<@UB3BGTV63> Maybe you have some examples of this implementation?
Now I'm stuck on the add ssl listener for NLB.
And also, some problems I have with add alias to NLB form Route53 ...