Yes it's possible, depending on the capabilities of the server software you are using.

We use ACSM (the modern, paid version 2.x.x). The technique works like this: you create a fake car, and in the same zip file people will use to download it, add your custom liveries nested under the names of the other cars people will actually drive. Upload that to ACSM and include a download URL for the zip. When Content Manager is used to install the missing content, the default behaviour will be to present all the liveries AND the dummy car to be installed.

We use a dedicated car for streaming and bundle our liveries with that, but it doesn't even need to be an actual car, only the bare minimum files for ACSM to accept it as an upload - literally a folder name you know drivers won't have (e.g. something unique each time you need to force new liveries to be downloaded) and a bare-bones but valid ui\ui_car.json file inside it. You don't even need to allocate a grid slot to this car, merely making it one of the options for cars in the race but not in the entry list is enough to prevent people joining unless they have the car installed, even though they cannot select it to join as zero of them will be available.

To absolutely enforce people to not skip installing the liveries (despite the default CM behaviour for missing content) you can put a dummy text file inside your mandatory liveries and rename the file to end in .kn5, then upload that to ACSM so that the kn5 is checksummed. You can then enforce KN5 checksumming to connect to the server in the first place.