Ahh I figured it out!
So, unfortunately, the page that shows you the custom domains is not where you need to be making your routes.
The correct procedure is to create an API (or use an existing API, and modify the resources) and give it a proxy resource, and a plain GET method that originates from the root path.
First, go to your API GateWay console, and create a new API.
Then once you give it a name, and choose the type (regional, or edge), it will show you the resources page
Here, you will do 2 things: Create a catch all proxy resource, and also a get resource to the root path.
Step 1: Make a catch all proxy resource:
Click Actions, and choose Create Resource
On the wizard, click Configure as proxy, and give it a name. Leave the resource path as it is. Then click create resource. The {proxy+} is notation that tells AWS that this resource should accept any path that has anything after the /. This means /test will work as well as /test/1/2/3/etc. However just / alone will not work!
Next, it will take you to this screen where you choose your integration type. We want lambda, which is the default. Make sure to select the correct region, for me the default was the right one. Then start typing in your lambda function name, and it should dynamically pop up a list of your lambda functions. select the one that you want for your application. If that doesn't work, you can copy and paste your lambda ARN from the lambda function console. Click Save.
Step 2: Make a get resource for the root path
Click the root slash at the top, right under where it says resources. Then click actions, and choose Create Method. It will pop up a little selection thing under the root slash, and there you should select GET, and then click the little checkmark.
Here, make sure to check Use Lambda Proxy Integration, and then the rest of this form should be the same as the last one you did. Just select your region, and your lambda function, and click Save.
Step 3: Deploy
Once that's done, go to actions, and choose Deploy API, give it a name for a stage, and some description, and then you are ready to attach this API to your custom domain.
Step 4: Attach
On the left tab scroll down to where it says Custom Domain Names, and create a new domain name (or attach it to an existing one if you have it)
Enter your domain name, and choose regional or edge. Then choose your certificate (there are many good guides for how to make a certificate through AWS)
Once you click save, it will look something like this:
Click Show Base Path Mappings, and then Edit.
In the path field just leave a slash, in the Destination field, choose from the dropdown the API that you just deployed. And on the right, select the stage that you made when you deployed your API.
Lastly, it will sit at initializing for a while, so while you wait for that, remember that you need to make a route53 record set for this domain, and map it to the cloudfront target URL that the API GateWay gave us. This target url looks like: www.u10dsa3s5iovdk.cloudfront.net. Copy that, and go to Route 53, Choose the hosted zone for your domain. Create a record set, and give it the same name as the domain you just created, so if you made www.example.com, in the name field of Route 53 you need to type in www. or if you made test.example.com you need to type in test. Then choose Alias: Yes, and for the Alias Target, paste in the cloudfront url from API GateWay.
When the custom domain name is done initializing, you can make calls to www.example.com as well as www.example.com/anything/else/you/want/to/put/here
Hope this helps anyone who was stuck as long as I was. Please let me know if there's anything I missed, or if something is inaccurate.
