Hey Patrick,
It would have been interesting to also read your approach first. Anyhow, here is how I'd think about this one (and assuming that you look within one country, otherwise you'd need to segment a bit more granular)

1) Look at the overall car replacement rate in your country (# housholds * avg car/household). We can then think about adjusting for decreasing/increasing growth in the overall market for cars. You might also consider that premium cars are more likely for corporate and limo service so the household approach is probably under estimating.

2) Estimate the fraction that is for premium car (obviously we would need guidance/assumption on price threshold for a premium car)

3) Estimate what market share an online car selling would get in the mid term. I'd have first a qualitative discussion on pro/cons of online sales for premium car, and then use other industries to triangulate an appropriate % of market share (such as luxury watches, private jet charters, or extreme such as Zalando with the idea that you'd difficulty get close to that for premium cars)

4) Estimate a time ramp-up to reach this mid-term market share from 3). Linear is the easy approximation but you might think about a hockey stick curve.

5) Combine all the elements to get your market on the first year.

Let me know what are you thoughts and how you'd have approached it.

I will basically do three steps to answer the question:

• Clarify the definition of online premium car sale market. Is it bounded by the online marketing effort, online financial transaction, or online customer service? Does this online shop operate like craigslist.com type info hub, or a shift.com type digitalized dealership who provide complementary test drive services?
• Estimate overall premium car sale in US. i) estimate overall volume of premium cars in US; ii) estimate lifetime of a premium car for new car sale calculation; iii) estimate average duration of premium car ownership for used car sale calculation; iv) sum up the new car and used car sale for total premium car sale calculation;
• Estimate the factor of online/offline premium car sale in the first year. i) estimate the factor for the corporate buyer (car rental company), ii) estimate the factor for the individual buyer; iii) estimate the ramp up speed for the factors respectively.