You have a couple of options. On your MS220 switches you could move to 802.1x port authentication. This means only authenticated machines will be able to attach to your machine. This is the most secure but also the most complex to setup.
This is typically done with a RADIUS server and a Windows AD domain, but you can also use Meraki Authentication if you have a small number of machines.
https://documentation.meraki.com/MS/Access_Control/MS_Switch_Access_Policies_(802.1X)
The next options are around group policy. You could make the default VLAN be a VLAN that is not conncted to anything. And then apply a group policy that overrides the VLAN and puts the user into a working VLAN.
You could also use a similar approach where you change the default L3 firewall rules to "deny any" and then use group policy to override those firewall rules to allow access.
https://documentation.meraki.com/zGeneral_Administration/Cross-Platform_Content/Creating_and_Applyin...