Can you give a bit more detail around this? Lets say a student wants access to youtube.com, they fill out a form, they are granted access for....24 hours?
It wouldn't give them a splash page to deal with, but assuming you could communicate a Google form out to the students a slightly manual proposal would be as follows:
(this proposal assumes that site restrictions are being done via group policy, and there are two group policies here, Student_Filtered and Student_Exemption which allows access to the URLs in question, but you could tweak this for certain URLs or groups of URLs)
->Have your school utilize a Google form to submit their request for access, the form puts the student's request onto a spreadsheet that the teachers can view (could be either for 24 hours or with an end date) and sends an email to the teacher to go approve it
->If the teacher approves they mark that on the spreadsheet, then the teacher goes into the Meraki dashboard and changes the student's Group Policy from say, Student_Filtered to Student_Exemption
->Every morning, a teacher or admin at the school checks the list of who is in the Student_Exemption and if the approval is every day they reset everyone to Student_Filtered, or if there are end dates in the spreadsheet they look for anyone who is past their permission date.
You could also automate this a bit more with the Meraki API, but doing it this way only really requires a google form, very basic dashboard knowledge and 2 minutes of work per day by a teacher/teacher assistant/admin.