Hi Jordan,
No, it's not possible to transfer your Free Trial subscription over to "Microsoft Learn Sandbox" directory, and you wouldn't want to.
Microsoft Learn Sandbox directory is used for the free, temporary (1-4 hours duration) Concierge subscriptions that are created when you Activate a sandbox in a Learn exercise.
What you can do instead is, next time you activate a sandbox, after you finish solving the puzzle, reviewing permissions, etc., open a separate browser tab and navigate to the Azure portal. In the upper right corner there is a gear icon, click on that and then click Switch next to Microsoft Learn Sandbox.
For exercises that are supposed to be completed in Azure Cloud Shell, open separate browser tab, browse to https://shell.azure.com, use the gear icon to switch to Microsoft Learn Sandbox (you may need to click the gear icon twice to see the list of directories), then navigate again to https://shell.azure.com if necessary.
When prompted, click Bash (sometimes an exercise has both PowerShell and Bash. You can switch between them as needed using button above cloud shell window).
Next choose No storage account required, for Subscription select Concierge Subscription, and click Apply.
At first the above extra steps may seem a bit confusing, but you will quickly get used to it, and it's an important skill. Knowing which Azure directory you are in as well as which subscription you are using at any given moment, is key and will help you later when doing actual paid work with Azure.
In regards to your Free Trial subscription, this will allow you more freedom to practice. First habit to learn is to create a resource group, create resources within this group, play around with them for learning purposes, then finally delete the resource group. This will help keep costs to minimum.
Every time you spend time learning, make sure the last thing you do is delete any/all resource group(s) you created and verify that they deleted successfully. Later, when you are more experienced, you will know which resources cost nothing (or very little) to leave around, but in the beginning it is best to delete everything after each learning session.
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP