Per Derek Law's old answer (Trail version of ArcGIS server installer), esri was (not sure if they still are) providing evaluation windows for ArcGIS Enterprise using AWS. However, that was three years ago when the deployment was still rather new, but it can't hurt to visit their site (ArcGIS Enterprise | Enterprise GIS Mapping Platform) and try and start a chat with the customer service rep to see what can be worked out.
If you don't mind me asking, what are you planning to do with the ArcGIS Enterprise license? Trying to learn the software? Create Web Map / Apps? Seeing if it works for your business? Knowing the why might help get you a solution
Normally the best way is to reach out to your local distributor. ArcGIS Desktop (ArcGIS Pro) and ArcGIS Online trail software can be downloaded from Esri website, but ArcGIS Enterprise (or ArcGIS Server in your case) will require a test plan and some personal attention from your distributor.
If you just need experience working with services, you can work with https://sampleserver6.arcgisonline.com/arcgis/rest -- if you need to get experiencing administering the AGE deployment, then contacting esri is your best bet.
FYI, a couple of other training options;
1. Esri Instructor-led training ArcGIS for Server: Site Configuration and Administration (3 day class)
Hope this helps,