Yes, this basically works as described in the original question using the Subscriptions module. You can simply add subscription an non-subscription products to a Sale Order. Those with the subscription flag will be re-invoiced by your subscription plan.

You can refer to the documentation on this topic here: https://www.odoo.com/documentation/18.0/applications/sales/subscriptions.html
A summary of the configuration an behavior is visualized in the tutorials as well: https://www.odoo.com/slides/20

Now, I don't remember by heart whether the 'first service will be invoiced at the end of the installation' part is described in there as well. If it isn't: 'end of installation' isn't really something Odoo would know without you telling it. To have this work, you would want to define your 'first service' product to have an Invoicing Policy other than Prepaid/Fixed Price so you can either track the completion of the initial setup using a Milestone or set the 'Delivered Quantity' manually (next to other options).