S3 access logs alone are not sufficient to replicate this pipeline. This pixel is stateful (for the anonymous user ID) and S3 access logs don’t include arbitrary headers, in this case the cookie with the user id. Fastly would let you eliminate API gateway, Lambda, and both Kinesis steps.
API Gateway by itself is $3.50/million requests, which is 2-4x more expensive than Fastly at $0.75 - $1.60/million