You probably should check if there is a difference between the full cash car price and the car price with loan first. And determine the depreciation per year.
The opportunity cost of paying for a car in full cash is that you could have use the difference between the downpayment and full price to invest in something that can get returns and cover the interest payments. Given that a COE in Singapore is valid for 10 years, the returns for an investment over that period might be reasonable after accounting for the interest payments. Typically a car is considered a depreciating asset.
You could pay the downpayment and get a car loan first. Then pay off the loan in full a while later if you decide that you prefer not to have an outstanding loan. Do note that there are finance charges for early repayment of the loan. Typically lost interest payments and other admin fees. Will have to check with financing company or salesperson for more details.
Or just pay in full and enjoy the car.