Can we index our site in google in 1 day or even 1 week?

Lot of advertisements intenet that the provide service to index sites in 1-day,3-day like wise. Is that really possible?

Indexing by who? My preferred method of search is Google so if that’s what you’re expecting then use Google and do a search about indexing and the answer to 1 day is no.
If the advertisement is for a search method that no one uses who cares if your site shows up in one day?

You need to generate a sitemap file (there’s tools to create them), and submit it through the Google Search Console, which is a free service you do need to register for. If you’re not able to generate a sitemap because your site is hosted somewhere the sitemap generator can’t crawl, you’ll just have to wait for Google to find your site the usual way.