Is it possible to make money...

Yes of course, you can get them to send you an email, etc. But it would make it less efficient without having an actual webpage for what you're selling.

Not only is it possible..., yes, it's possible.

In my conventional business of engraving, I get customers from social media. So it's possible

Yes, it is possible but for that your social network should be very strong and matched with your niche.

So as far as building a email list, redirecting someone to a email Address or my blog would be more ideal?

If you did want a cheap way to have a domain without having a domain: you can get a domain at namecheap for 88 cents and redirect it to your offers. You can either redirect it to a rotator so you can show all your offers or just redirect one at a time. I suggest the rotator if it makes sense with the name and the offers. (I.E. it only works if they are all related to your name.)

What's the strategy without website? Anyone?

Without a website, you would have to drive target directly to your affiliate link. This can be done via social media, solo ads, etc... the bad news is that you have zero idea about the stats except what your offer indicates. You would not be able to track the hits and stuff. Another method without a website is to make Youtube review videos and put your link in the description. Youtube does not like affiliate links so you would need to cloak it first.

OF COURSE, social media is even a great stepping stone to make money, before you move further to building a website.

Yes, absolutely! Just study your market on Facebook, and promote your products/services to them. You can also create a page or join groups to establish presence on this platform. Basically, Facebook is a great place to start off if you still don't have a website to start with.

yes, its possible since lot of social media helps to make money..

Hi mate,

great question and the short answer is: Yes - 100 %.
There are various methods that you can use in order to use social media to generate revenue.

There are both free and paid methods that you can use - very much depending on your budget and the time that you have (or want to invest).

Free methods:
Engage in product related groups and engage with the members. Show them that you are an authority in the field and that you have good knowledge with them to share. As you get more and more accapted you have the chance to place links (ref links to products and services) and people will have an genuine interest as to what you have to share as an expert in the given field.
You could also start a group about let's say paleo recipes. As the group grows and you share knowledge /tips / guides and they accept you as an authority you can (again) place links to product pages or services.
Obviously both of these approaches take quite a bit of time before you can expect any results.

Paid:
Let's take Facebook Ads as an example. I personally know multiple people that make a killing on facebook without website. They simply know how to target the right audience on facebook at a cheap price. This being said: These guys are highly experienced in this field and spent thousands on ads in order to master this craft. Just throwing money on ads won't get you far. IF however you master the game you can build a profitable, sustainable business from it.

I personally always like to take the route over a website in order to catch the lead. That way I can contact them again and again and again without spending a dime.
Nowadays you don't have to know how to program website. You can either hire a freelancer on websites like upwork or you design a website yourself with the easy-to-follow drag and drop tools from services like Leadpages.

Of Course..Its Possible, Many social medias helps to promote your service and make money!!!