Why was The Big Bang Theory given that name?

Beyond the obvious fact that the show and its characters are science-themed, I would suggest that some insight can be found through the lyrics of the theme song by The Barenaked Ladies:

Our whole universe was in a hot dense state,
Then nearly fourteen billion years ago expansion started.
wait...
The earth began to cool, the autotrophs began to drool,
Neanderthals developed tools, We built a wall (we built the pyramids).
Math, science, history, unraveling the mysteries,
That all started with the big bang! Hey!

The Big Bang theory (the theory itself, not the show, and leaving aside actual discussions of inflationary cosmology) is about unraveling the origin and development of the universe. The Big Bang also represents the beginning of the chain of events that lead to the development of humanity.

We developed tool use and changed the landscape around us by building things. We developed math and science as disciplines to help us understand our reality, and the study of history brings that understanding a step closer to us by focusing on our own development and impact on our species.

As we unravel these more prosaic mysteries, so too do we unravel the mysteries of the human condition. Comedy and drama have long been ways we as a species express thoughts and concepts about our humanity. The show addresses many of these themes: honesty and communication, love and friendship, cooperation and competition, fear and confidence, etc. In its own small way it contributes to the understanding of the mysteries of being human, which all started with the Big Bang.

The main characters of this show are scientists (2 physicists, an astrophysicist, and an engineer). Most of the episodes are also made to sound like scientific theories or terms. I'm not sure if the directors and producers ever revealed why they named it so in any interviews, because I am not able to recall any episode based on big bang theory.

I can just speculate the following reasons:

1. Maybe it's because of the fact that those nerds (scientists) evolve slowly to become common men (or less nerdy). You can compare the season 1 characters to season 8, it's a big transformation.
2. Maybe someone wanted to exploit the double entendre usage of word "bang", which Leonard seems to do with Penny in at least the initial episodes. In fact, it was the main theme of the TV series when it started, then slowly "Sheldon" became the central character due to his popularity.
3. Another reason can be that they wanted to give the impression that we are learning some scientific things from Sheldon along with good comedy.

I think the show title is a play on words. The Big Bang Theory is an explanation for the birth of the universe. But also, "bang" has a sexual connotation. In the beginning, Leonard was attracted to Penny, but she seemed to be out of his reach socially. If he was to have a sexual encounter with her, his social status would be elevated. So in a sense, penny is the Big Bang.

While the show outgrew that premise pretty quickly, early reviews seemed to focus on the romantic aspects and the fact that Penny was out of reach for Leonard. Here's one from 2007:

The solid if well-worn setup is that of the beauty among the beasts, or in this case, geeks. Math geniuses Leonard (Johnny Galecki) and Sheldon (Jim Parsons) have been content to spend their days in their apartment working on formulas and playing Klingon Boggle. Then Penny (Kaley Cuoco) moves in next door and Leonard invites her over to lunch — and the equation of their lives changes.

If Bang is going to win you over, it will happen soon after that invitation, when Penny plops onto Sheldon's favorite spot on the couch. Everything that works best in Bang is right there: Cuoco's slightly confused, sweetly bemused response; Galecki's mix of longing and exasperation; and Parsons' fresh, show-stopping take on socially out-of-whack brilliance.

And another, also from 2007:

THE BIG BANG Theory" isn't exactly an original idea — nerdy guys meet a beautiful woman.

They hang out with a couple of other Cal Tech geniuses, Howard (Simon Helberg) and Rashesh (Kunal Nayyar). They can all speak Klingon, but they can't talk to girls.

But then the gorgeous-but-not-too-bright Penny (Kelly Cuoco) moves into the apartment across the hall from Sheldon and Leonard. Leonard falls in love, but Sheldon is more than skeptical about his chances with Penny.

"What makes you think she wouldn't have sex with me? I'm a male and she's a female," Leonard says.

"Yes, but not of the same species," Sheldon replies.

And when Leonard imagines a future with Penny, he says, "Our babies will be smart and beautiful."

"Not to mention imaginary," Sheldon deadpans. (Keep an eye on Parsons — he may well be one of the breakout stars of the season.)