What has been the relationship between ancient India and ancient Japan? Have these two come in contact in ancient times?

Ancient times?

Japanese Civilization, as far as the term can be used, began roughly in the 2nd Century BCE. While we do hear from Japanese kingdoms and such from the 3rd Century CE, these mentions only really become concrete in any way post the 6th - 7th Centuries.

Thats when the Late Classical Period of Bharata History begins, a full two millennia after “Ancient India”.

You still get a few common links but no more. The standard “Japanese” temple is basically a particular form of early Classical Hindu Architectural style for all purposes, of the style favoured by the Kiratas, pre-Classical Kashmiras, and certain Dravida peoples. The oldest Buddha statue in Japan, which is supposed to have entered their islands in the 7th Century, is a 5th Century Gupta figurine from the Mathura school.

Both influences clearly went through Chinese intermediaries with zero sign of direct contact. Classical texts don't even mention Japan, even though they had a rough idea of the political situation in contemporary Korea or Garyadesha.

That's your answer. There was zero interaction between Ancient India and Ancient Japanese, if only because “Ancient India” ended long before large scale human settlement in Japan.