What is better for proxy and add athorization header to my calls? Lambda or Api Gateway

Hello guys Im trying to decide among some architectures for my serverless application.
I have two backend endpoints in two different applications hosted on AWS and both of them need a static authorization header to work properly. So instead of creating a node server for my application just to proxy my same-origin requests and add the header Im thinking about doing that serverless.
What would you suggest me to do:
Front -> Api gateway -> my other endpoints
Front -> Lambda -> my other endpoints

I expect a high traffic for this application but the frontend call will always be over https, same origin and most of the time, by anonymous users


I suggest you to either go with:
Front -> Lambda -> my other endpoints
If you want to go with the conventional option of Amazon Web services. This is the featured offered by AWS it self for a less technical guy. So, the person can easily undergo the hosting process all by himself.
However, If your are technical enough to handle the technicalities of hosting server then you may also go with:
Front -> Api gateway -> my other endpoints
Serverless will work fine in both cases. I hope you have your answer now. If you are referring to something else then do let me know.

If you are not utilize all feature of API gateway such as Auth, Caching, Logging, Monitoring Throttling, Bursting Elastic then you should consider using Lambda as proxy with ALB to save cost. Refer to this article for more detail about the serverless pattern for AWS if you want to explore more