General Timeframe

Shirobako's main plot - not counting the very first scenes where the girls are still in high school - most likely begins on the October 2, 2014. (Funnily enough, Shirobako started airing IRL one week later.) There are a few bits of information that confirm this:

1. The date

A few consistent clues in the first episode reveal that the October 8 of the current year is a Wednesday:

[Episode 1] The calendar on Aoi's desk shows October, including the 8th being a Wednesday.

[Episode 1] Aoi's desk phone is shown, which displays the date and the day of the week: the date is the October 8 and the weekday is Wednesday.

[Episode 1] The date is confirmed again later during the same episode, when Honda looks at his watch. It displays Wednesday and the 8th of an unspecified month.

October 8 being a Wednesday leaves, within a generous time frame, the years 1997, 2003, 2008, 2014, 2025 and 2031.

2. Exodus air dates

This is important because the main plot of Shirobako begins on the day when Exodus's first episode airs. The first half of the show also ends one day before Exodus's thirteenth and final episode airs.

It is confirmed on at least two separate occasions that Exodus airs on Thursday nights:

[Episode 9, November 17] Honda: "Episode 8 was finished last Saturday. It's scheduled to air on Thursday."

[Episode 12, December 24] Katsuragi: "It's going to air tomorrow night!"

See November 17, 2014 and December 24, 2014.

To confirm the point from above: in any of the aforementioned years, December 25, the day the final episode of Exodus airs, is a Thursday.

3. The year

I think I remember a calendar displaying 2015 in one of the episodes in the second half of the show. Alternatively, during episode 12, Aoi says she was two when "Ava" first aired in 1995, meaning she was born in 1993.

Kanno: "How old were you when Ava aired?"

Aoi: "Pardon me, but what year was the original TV series?"

Kanno: "'95."

Aoi: "Then I was 2."

See December 12, 2014.

Now, my knowledge about the Japanese education system does not go beyond what I have picked up from watching various anime, as well as skimming the Wikipedia article. Basically, the school year in Japan begins in April and children enter first grade when they are six (Wikipedia), which means Aoi started going to school in either 1999 or 2000. This then means Aoi, Ema and Shizuka, who graduated together, did so in either early 2011 or early 2012. Immediately after the graduation scene, there is 2.5-year time skip which leaves us with either late 2013 or 2014.

"2.5 years later"

This checks out beautifully. Aoi, Ema and Shizuka, graduated in 2012, Misa in 2013 and Midori in 2014. By October 2014, Aoi and Ema are working as Musashino Animation, Shizuka is a voice-actress-in-training while working part-time, Misa is doing 3D work for a game development company and Midori is going to university.

This is where Shirobako's main plot begins.