Can I make a Cheesecake without using cream cheese?
Cheesecake is essentially a baked custard with that substitutes cream cheese (and often some sour cream) for the dairy ingredient.
After all, a basic custard recipe is just milk, sugar, and eggs with some kind of flavoring added.
The cheese is the thing that gives cheesecake it's distinctive texture. Substituting cream and corn starch is going to end up with a much more pudding-like consistency.
All that being said, there are a number of recipes that substitute the much milder Mascarpone cheese in place of about half of the cream cheese. This may be sufficient to get you a milder sour flavor without drastically altering the texture. You could also give it a try with all Mascarpone, but you might be pushing into that pudding texture again.
Also, be prepared for the added cost with Mascarpone, which tends to cost 2-3 times as much as cream cheese.