We have a domain and a hosted website attached to it.
For one of our product, we bought a second domain, which forward to our main website.
Is there anyway to have search engine index or find that domain?
Yes there is. As long as your 2nd product's website has a hyperlink to it from another indexed website, then the search engine's bot will find that domain. The bot's author will have tuned their bot to either reject your website - based on rules that the bot author or search engine company doesn't want to see in their search results - or accept your website & add it to its search engine index. (FWIW, That's how my search engine bot works, with my search engine index.)
Both John & cloestnoc have valid points about what you shouldn't do, as those actions will boost the likelihood that your 2nd domain would be rejected by Google. The reason is that search engine authors don't want to have duplicate content listed in their search engine results pages (AKA SERPs). SERP screen real-estate is very valuable screen real-estate. Duplicate content would be frowned upon by users, because they'd think that they were looking at a poorly built search engine... which isn't the case.
What you don't want to do is link your main website to your 2nd product's website & then have that 2nd product's website point back to the main website, with the intention of automatically meta-refreshing to the main website. That is known as a "web ring" & search engine authors do not like those. When bots crash, search engine authors will look at your website to see what you've done to crash the bot. Then they will tune their bots to make them smarter & better, so that they won't crash again. That's where they can add a way to penalize people who build websites like that, which crash their bots. That's the "SEO ding" concept. Search engines ding/penalize sites which crash their bots.
Historically, some webmasters have built sites with 10 - 50 round-robin linked pages, to intentionally trap bots & artificially boost their SEO values. That tactic is frowned upon & will most likely be a really good reason to automatically reject indexing a website. Bot authors do built their bots to detect & break out of web rings. So be careful that you don't build one for the express purpose of boosting your SEO ranking. It's better to write quality information on your website, where people would organically want to create a link to your site, in order to use your site as a reference guide or explanation for their visitors. Writing quality content will definitely help boost your SEO ranking value!
Here are some useful links for you:
These links are interesting to know about, but you should probably bookmark them for perusing in the future: