The simplest solution is to add a calculated field to the model which uses the date in question as its value, but this requires that you edit the formula each time that you use the model.
The next possible solution is to employ a runtime parameter calculated field, which will prompt you for a date value upon opening the model. Even if you don't know the value at the time, it's easy to revise the value once the model is open by double-clicking the field in the Table window.
A third possibility exists, but requires two passes (two models). In the first model you'd add a text field to be used a common key between the two model. Assign the field a fixed value of "KEY". Build a new filter using the expression:
Hide all of the fields except the KEY field and your date field. Build a project export to produce a file with this one record. Save and close the model (as a variant of your original model) and the project.
Now open the original model and add the same KEY field, and then add an external lookup using the KEY field as the connection between this model and the external lookup file, importing the KeyDate. Now the KeyDate will appear in every record, and you won't need to fiddle with updating the value manually in your model yourself every time. Save this model.
As with every multiple pass/model solution, it's easiest and best to create a batch file to run the various models in an automated fashion.