That's why I'd like to improve the beginning of the map with additional civs. Apart from Lombardy (as in RFCE++), I don't have any specific civs in mind.
I have a few ideas for your consideration:
1. Visigothic Spain/Kingdom of Asturias
They would exist from the get go as a reasonably well-established kingdom throughout Spain (minus the Suebic kingdom in the northwest). There's potential for some interesting early game events with the French as Clovis kicked the Visigoths out of southern Gaul at the beginning of the 6th century. For UHV ideas, there's the conquest of the Suebi, the Visigothic law codes, and a cool ahistorical goal of surviving Muslim expansion as a starting point. You could also/instead play into the survival of the Visigothic kingdom as the Kingdom of Asturias. Maybe you could even do something like reconquering the lands Clovis and the Franks took from you. Maybe you could make an Ostrogothic goal and retake Italy. There are some neat options for the Goths, I think.
2. Anglo-Saxon England
They're another nation that would exist from the get go, but since it's so early in their settled history, I think it's fair to justify them as having only one starting city as opposed to the Visigoths, who would start with several just like the Byzantines. For UHVs, I think there are some pretty obvious options here in first acquiring the lands of Wessex, Mercia, East Anglia, and Northumbria; surviving the Viking invasions; and finally repelling William the Conqueror.
3. Avars
Unfortunately, I know a lot less about the Avars than I do the Anglo-Saxons or the Goths, but they would be a good add for Eastern Europe
4. Ostrogoths/Lombards
I'm going to start by saying this should be the Lombards, and I think you even already added the Lombards. They're a good add. However, the Ostrogoths and Theodoric the Great absolutely deserve some representation, even if it's just some independent cities. Theodoric the Great truly earned his name and built a kingdom out of the ashes of the west that came awfully close to just being a continuation of the empire. More independent cities in Italy at the very start to represent Theodoric and the Ostrogoths would be a good add.
5. Vandal North Africa
This is definitely pushing the boundaries as a playable Vandal faction is quite ahistorical since they were gone by 535. However, they do have a couple points going for them that others, like the Ostrogoths or the Suebi, do not. First, they don't really have competition for their historical bounds for quite some time. The Byzantines, Arabs, and Cordobans are going to be hard-pressed to make their way there in time enough to kill them off before they've existed for several hundred years, and later nations like the Moroccans or Sicilians arrive late enough that it wouldn't be an issue. That said, I do believe you said you added a Belisarius conqueror event, but I also believe you said it was focused on Italy? Anyway, this lets them occupy a niche on the map that's largely unoccupied for much of the game, so even if they're an ahistorical add, the gameplay addition is worth considering. If you opt to not include them, a strong, independent Carthage from the get go would be a good representation for the Vandals.
6. Independent Cities
In general, I think the fall of Rome is overexaggerated in terms of overall urban collapse. Yes, things absolutely regressed as central authority broke down. And in some places, like Roman Britain, things absolutely devolved into barbarism rather quickly, and it took time for things to be restored. However, in places like Visigothic Spain, Frankish Gaul, Ostrogothic/Lombard Italy, and Vandal North Africa, old Roman cities continued to serve as administrative centers for these new kingdoms. There is a strong argument for, even if you include none of these options as playable, including many independent cities throughout western Europe to represent these successor barbarian kingdoms. On the other hand, planning out your city placements is one of the cooler features of Civ, so if you put too many independent cities on the map, this can easily get lost in the shuffle. There's a balance somewhere that manages to accomplish both representing the barbarian kingdoms and city settling, but I do not know what it would look like.