Does Google sandbox exist?

Does Google sandbox exist?

For years now there has been a lot of debate on whatever a Google sandbox exists. 

What is Google Sandbox? 

Well, in short, it ma e is some kind of flagging don't by Google to doubtful websites, a sort of probation period where Google probably keeps an eye on your website until it makes sure you deserve better rankings, getting out of the sandbox. 

Sandboxed websites don't get deindexed, they just get way worse rankings and lower organic traffic than expected. 
I personally experienced the "sandbox" effect myself. 10 years ago or even more it was pretty easy to rank a new website for a specific keyword if you had a small network of websites. 
So I started this new website and right from the start I gave it side-wide backlinks from all the other websites I owned plus asking friends and contacts with multiple websites to side-wide link my new website. 

I start ranking in no time! I even got top 3 positions for all my main keywords. This didn't last long, just a few week or so until Google penalized me or got me into the sandbox. Don't know exactly which one of these happened but my rankings drop as well as my organic traffic. I then removed all the backlinks I previously implemented and the website started ranking again, this time a lot lower than it previously did but at least I was begging to see some organic traffic. 
So I figure this was a Google Sandbox experience. 

Dose Google Sandbox really exists? 
Well, Matt Cutts admitted it to some degree as far as I know, which made it true for a lot of webmaster and SEOs out there. 
Recently Gary Illyes from Google was asked if the Sandbox really is a thing and he denied it. 


Well, yeah, sure Gary! Maybe you guys at Google don't really call it "sandbox" but I definitely believe you have some kind of algorithm in place that acts similarly to what most SEOs describe as Google Sandbox. 

Getting out of Sandbox. 

So you may think to yourself, how do you get out of the sandbox once you been hit? Well, I don't really know. I only did this for my website on which I had full control over all the backlinks but also I did it for a client. The trick is to remove all the spammy backlinks that website may have. And that can be very challenging, especially if you bought blackhat links from dubious sellers. 
Good content + a clean backlink profile = getting out of Google's Sandbox in theory. 

What is your experience with Google Sandbox, do you think it exists in some for or the other? Have you ever had a site that got sandboxed? What kind of methods did you use to get it out?