Would be cool if I could see some images too, would be cool to see a dog from the past CGI'd to how it'd have looked like :)
This is my area of expertise. (he says humbly... But honestly I don't know a lot about much but have obsessed over dog history for decades and can honestly say I don't know of anyone who analyses this niche topic as keenly as I do). I'm not in the position to make a good post but will just urge you to search for "the dogs of vindolanda", which is a scientific article about dog skeletons dug up from an ancient Roman settlement in Britain (and mentions other dig sites around ancient Rome). Much less variety than today, but still significant variety for functional purposes. Rather than "350 breeds" there's about 8 distinct types recovered from these sites.
Another great resource are writings about dogs by ancient romans. They don't talk about breeds but rather the dogs of this area and the dogs of that area. Like each of the people they conquered had one type of dog each, basically, and Rome amassed a variety by absorbing them from these conquests. You see the earliest references to scenthounds and livestock guardians and the like in these writings, and get some idea of where each originated. Sighthounds it seems were the most common and most widespread, as this and that region mostly all seemed to have wirey fast hounds for the chase, and then it was noteworthy and somewhat peculiar when a certain people would have a type of dog which wasn't very fast but used it's nose or laid with the sheep or whatever.
I'll get back to you with the links I'm referring to when I can.
This topic pops up quite a bit from time to time -- while you're waiting, you might be interested in these previous threads:
What were historical dogs like? by /u/xuankifoods, discussing the distinction between dog breeds and dog types
What do Ancient and Medieval sources say about the care and training of dogs? by /u/sunagainstgold, on dog breeding in the Middle Ages