Have the Cloverfield films drawn from Half-Life or earlier base material about aliens invading from a portal?

They are both very lovercraftian. A story that would be almost verbatim taken from HP would be about a man who get curious (almost like scientics) of the unknown, they unleash the monster(s) (invoking it, making portal, waking up), mankind cannot destroy the beast, man goes mad for even acknowledging the beast (or start collaborating in different ways), monster wreak havok, get bored and get back to the sea.

From a interview with a writer for Half-Life, Marc Laidlaw Here

The Lovecraftian influence is buried pretty deep in Half-Life—perhaps you can spot it in the sense we try to create of mankind being a tiny speck in a vast cosmos. The most Lovecraftian passage is probably Dr. Breen’s speech at the end of Half-Life 2, when he is trying to entice Eli with glimpses of the wonders he has been shown by the Combine. This sort of teasing view of things beyond imagining is one of Lovecraft’s techniques, on display most clearly in “The Whisperer in Darkness.”

But as you can see it's not very deep. The tentacles are pretty obvious, the terror from the deep (of space).

Here is a nice stock photo. I showed it to my Half-life friend and one that knows about HP.

https://www.dreamstime.com/man-looking-tentacle-monster-destroys-city-digital-art-style-illustration-painting-tentacle-monster-destroys-image155047946

One said it's Blast pit monster, second that this is shoggoth. I think someone who is very into JJA trilogy would say it's Cloverfiled.

As the other answers suggest, the concept of using portals with aliens the way that either Portal or Half-Life does is not an original idea and therefor it is hard to determine if they are "source influences" in The Cloverfield Franchise.

However, we may be able to speculate that there *could be some influence given back in 2016 JJ Abrams and his Bad Robot Production company were interested in making films for either Portal or Half-Life.

"We are having some really interesting discussions with writers, many of whom…once you said you’re doing a movie or show about a specific thing that is a known quantity you start to find people who are rabid about these things. As someone who loves playing Half Life and Portal, what’s the movie of this, it’s incredible when you talk to someone who just ‘gets’ it, it’s like, oh my god, it’s really the seed for this incredible tree you’re growing."-JJ Abrams

It's unclear what is happening with this now, as Star Wars and his new deal with Warner Media has taken precedent in recent times, but Abrams has been interested in, getting more and more into, the video game business and/or have interactive games to go along with feature films or TV series.

Cloverfield came out in 2008. The source material for Dr. Strange, which allowed Kaecilius to travel through portals, dates back to the 60's. So, the concept of "evil" travelling through portals is not new. I know A Sound Of Thunder (2005) played on a wrinkle of that , where travelling through a time portal altered the past, whereby creatures ended up inhabiting the Earth (thus, inadvertently bringing an "alien" species to Earth). The Gate (1987) could also be said to be a movie where creatures were brought to Earth accidentally through a portal.

So, it's possible Half-Life had some influence, but it certainly wasn't an original idea by that time.