Can I build a website and host it later?

Well, for a website - you need a domain and web hosting. Having both of them at the same time is not at all costly otherwise usually considered.

If you do not have any domain extension preference, you may have a multidomain, unlimited web hosting with email accounts for as low as INR 399/USD 6.99 Per Year. Here you get an XYZ domain and Web hosting for one year.

Is it pricey? Its less than one visit to a restaurant!