This is of course not the only way to earn coins. You can just play online and earn them. Make sure you do not end up wasting time or ‘showboating’ when you are ahead so you can quickly farm up the coins and move on to the next game. If you think you’re good, then spend tickets to enter tournaments which can have massive prizes.
The best way to start earning coins quickly is to do the solo challenges which are not only very simple and easy to do, but also take a little less time. Since there are no free coins and the only way to Madden Coins get coins without doing anything is spending money, get used to grinding.
Take a look at your objectives and see the easiest ones. Keep doing the easy ones until the challenges become too time-consuming and just not worth the reward. After this, you can start the Longshot Story Mode which is another feature imported from FIFA (known as the Journey). Start doing the mode as it is not only extremely fun but also rewards you with decent free cards.