Is it possible to create a custom lookup field that allows multiple selects? I couldn't find an option for it.
I've created a Project object and was attempting to connect it with the Product object where the user can select multiple products for that project, but I think I might be treading down the wrong path (was going to try multiselect plus trigger, but the list of products is going to be way too big for that to be effective)
No, this isn't possible.
The standard method to implement something like this is what's known as a Junction Object. This junction object allows you to create the many-to-many relationship that you're envisioning as a picklist.
In your case the junction object could be called ProjectProduct__c and that object will have two lookups on it, one to Project and one to Product. This will allow you to link a project to many products and likewise, a single product to many projects.
Here's some documentation from Salesforce on implementing Many-to-Many relationships.
we can create multi select lookup using apex, i have created multi select lookup for one of my projects, please see below image
