I read an article about a Silicon vValley start-up company.

They are not a typical start up like companies with a bunch of guys in a garage codeing.

I read an article about a Silicon valley start-up/startup company.

They are not a typical start up like companies with a bunch of guys in a garage codeing.

この文章はほぼ完璧だったけど、指摘したいことがあります。「typical 」を使ったので、[bunch of guys in garage = typical startup company」という意味になります。でも、アメリカではstartupのイメージは結構いいと思います。僕がstartupを聞くと、小さいけどとてもきれいな、かっこいい会社を想像します。

I think [the number of] companies like this will increase in the near future since people around the world will try not to use plastic products.

Since you use "increase," don't forget to include "number." Usually, these two words go together.

They are not a typical start up like companies with a bunch of guys in a garage codeing.

I think companies like thisese will increase in the near future since people around the world will try not to use plastic products.

You are referring to plural "companies" so you have to use plural "these" here. If you want to refer to just the one company from the article you could use "this one".