I’m not an expert, but I may be able to point you in the right direction.
VLANs are for separating traffic so you won’t be able to ping from one VLAN to the default VLAN unless you have routing enabled to allow such traffic at a higher level.
If your switch is only a layer 2 switch it probably won’t support routing between VLANs, so the default gateway of the switch will need to be configured with an access list that will allow traffic from anywhere to your DMZ VLAN that you create.
If you have an advanced switch then you can do this routing from its management interface otherwise your router or default gateway will need to accomplish this.
I hope that helps at least somewhat