India won Cricket World Cup in 1983. I believe Cricket was not that popular in India before 1983. As Indians were World Champs, many were inspired to play cricket.
After this World Cup, Indians didn't performed to the expectations and popularity was fading. Then something special happened on November 15, 1989. Sachin Tendulkar made his debut in International cricket.
India saw a rising star and he was exceptionally good. Sachin performed so well that in 90's India was one man army. For most of the time in his career "Sachin kitne par hai?" (English: How many runs Sachin scored?) mattered more than the result of the game.
That’s how it has always been. Like since inception, cricket
has been perceived as more appealing than other sports. And with personalities
like that of Sunil Gavaskar, Kapil Dev, Azhar, Sehwag, Dravid, Sachin, Dhoni
and more, its popularity only spiked high.
As far the other sports are concerned, in recent times, they
did have climbed up in the spotlight. Like football, MMA, tennis and even
badminton boasts a massive following today. Nothing, however, comparable to
Media always focus more on cricket. Sponsors always put more
money in cricket matches. So people get to hear, see more of cricket. And since
more people are watching this sport, more sponsors and media will invest in and
talk about it. It’s like a cycle.
But it’s not bad. We shouldn’t be complaining about it. Like
in Brazil, Soccer is more popular; in USA, Football (rugby) is at the top;
people in Canada obsess Ice Hockey. Every country leans toward particular sport.
Cricket was acquainted with India by Brits, at some point in mid 1700's. The principal Indian Cricket Club "Oriental Cricket Club" began in 1848 and this you can call the beginning of Indian Cricket. By 1912 the other Indian groups that developed were for the most part dependent on religions - Hindus, Muslims and Sikhs, alongside the European and Parsees., who played a Quadrangular arrangement consistently.
Indians have always been fascinated with epics. The Mahabharat and Ramayan are read by people of all religions and both became runaway successes when they were turned into TV shows. More importantly, those two epics are deeply embedded into the psyche of a vast majority of Indians.
A cricket Test match, with its timelessness, leisurely pace and the option of a middle path (the draw) might have been some of the reasons why so many people in India took to the game so enthusiastically. A tightly-contested game of cricket is often called an epic.
India did not have a competitive Test team for a long time but the popularity of the game remained high and that is probably down to the fact that in the early years, Indian fans followed the game for the unique features that the game had to offer.
It's doesn't cost much to play cricket. Even someone from a humble background can easily pursue cricket. Players just need to arrange a bat and ball to play the game. Most players in India start their cricketing careers by playing gully cricket in their localities. Though the ball used in international cricket is a leather ball, gully cricket is played with a tennis ball or a taped ball.
Australia has a lot of land and hundreds of dedicated ovals which host football matches (of various codes) over winter and then in summer can be dedicated, full time cricket grounds with prepared pitches in the middle. Cricket grounds need to be dedicated cricket grounds for an entire season and there aren't many countries that have fields that can spend six months hosting cricket games.
The pitch problem is the reason cricket can't be played at Olympic level (even though it's frequently suggested) and the reason it's so hard to promote in other countries.
Compared to other sports, cricket has more number of coaching centres in the entire country. This factor is hugely responsible in drawing more and more young children, who aspire to be future cricketers.
Similarly, almost in each and every state there is at least one world class cricket stadium present whereas if we take a peek into football and hockey, there are only a few FIFA accredited stadiums and genuine astroturfs respectively, present in India.
This important factor also contributes to the increased participation and popularity of the sport.