$ sam build

...

Build Succeeded

Built Artifacts  : .aws-sam/build
Built Template   : .aws-sam/build/template.yaml

Commands you can use next
=========================
[*] Invoke Function: sam local invoke
[*] Deploy: sam deploy --guided

$ sam local start-api

Mounting Function at http://127.0.0.1:3000$default [X-AMAZON-APIGATEWAY-ANY-METHOD]
You can now browse to the above endpoints to invoke your functions.

2021-11-14 22:20:56  * Running on http://127.0.0.1:3000/ (Press CTRL+C to quit)

$ curl http://127.0.0.1:3000

{"message":"FastAPI running in a Lambda function"}

$ sam build 

$ sam deploy --guided
...

CloudFormation outputs from deployed stack
---------------------------------------------------------------------------
Outputs
---------------------------------------------------------------------------
Key                 ApiUrl
Description         URL of your API endpoint
Value               https://API_ID.execute-api.eu-west-1.amazonaws.com/
---------------------------------------------------------------------------

Successfully created/updated stack - FastAPIOnLambda in eu-west-1

$ curl https://API_ID.execute-api.eu-west-1.amazonaws.com/

{"message":"FastAPI running in a Lambda function"}