setup an aws api gatway with serverless - aws-api-gateway

Question

I built out my dev environment manually, I wanted to focus on logic and skip the learning curve on serverless, but before deploying to prod I want to standardize and parameterize my stack.
setting up my dynamodb tables has been straight forward, but I'm running into snags with deploying a new api-gateway.
I've been using aws codebuild to package layers for lambda functions and an s3 bucket to store my lambda code.
Let's take my dev-rest-auth api (custom authentication) as an example.
I have several resources for login/out, passwords and registration; most are protected by a custom authorizer (login/logout aren't) and all have cors policies. I'm using a custom domain account-api.dev.example.com I use several dynamodb tables for housing user data (let's avoid security discussions please, I'm not storing raw passwords and am encrypting using leading industry standards) and temporary codes (password reset & account verification).
to test serverless implementation I'd like to build a yaml file that recreates my existing infrastructure - so the first question is -- is that possible? Can I parameterize the deployment of an API gateway, with custom authorizer, custom domain, and several lambdas?
Next question is how?
Organizationally I'm breaking out my yml files by resource:
I have several dynamodb yml files that look like this:
Resources:
UserTable:
Type: AWS::DynamoDB::Table
DeletionPolicy: Retain
Properties:
TableName: ${self:custom.resource-prefix}-UserTable-${self:custom.stage}
AttributeDefinitions:
- AttributeName: email
AttributeType: S
KeySchema:
- AttributeName: email
KeyType: HASH
# Set the capacity to auto-scale
BillingMode: PAY_PER_REQUEST
This was a much earlier attempt (several months ago, from googling, but I don't remember where I found it or what it does) of standing up an API gateway:
Resources:
SharedGW:
Type: AWS::ApiGateway::RestApi
Properties:
Name: SharedGW
Outputs:
apiGatewayRestApiId:
Value:
Ref: SharedGW
Export:
Name: SharedGW-restApiId
apiGatewayRestApiRootResourceId:
Value:
Fn::GetAtt:
- SharedGW
- RootResourceId
Export:
Name: SharedGW-rootResourceId
I pull everything together in a serverless.yml file that references the resource files like this:
...
resources:
# S3 Bucket
- ${file(resources/s3/s3-static-host.yml)}
- ${file(resources/s3/s3-CodeBuildResults.yml)}
# DynamoDB
- ${file(resources/dynamodb/dynamodb-mealtable.yml)}
- ${file(resources/dynamodb/dynamodb-ziptable.yml)}
- ${file(resources/dynamodb/dynamodb-usertable.yml)}
- ${file(resources/dynamodb/dynamodb-passwordresettable.yml)}
- ${file(resources/dynamodb/dynamodb-accountregistrationtable.yml)}
- ${file(resources/dynamodb/dynamodb-restaurant_table.yml)}
# DNS Records (Route 53)
# TODO: Determine why DNS hangs
# - ${file(resources/route_53/dev_dns.yml)}
# Gateways
- ${file(resources/api_gateway/local_rest_auth.yml)}
# - ${file(resources/api_gateway/rest_auth.yml)}
...
I've seen several examples of connecting a lambda to a gateway, but it's not clear where the gateway is being created), it's also not clear how the lambda is being created/if I'd be able to reference layers/function code in s3.
I've seen some tutorials for doing this with aws amplify via the cli, but my dream-state would be that I could effectively create a new aws account, deploy this serverless and have my site up and running automatically - with just a little route 53 work to point to a new domain.