Can I file taxes if I don't have a job but have a child under 3...and if so would I receive any money
The following assumes you live in the United States.
If your income in 2019 was less than the standard deduction of $12,200 ($24,400 if married filing jointly or $18,350 if filing as head of household), you are not required to file a federal tax return (assuming nobody can claim you as a dependent). This is likely true for your state as well. You are always permitted, however, to file a return even if you are not required to. This is how you would get a refund of any money that was withheld from your paycheck if you had a job.
If you do file a return, you likely will get some money based on what you've told us. The child tax credit is a $2000 tax credit, of which $1400 is refundable. You get this credit for each child you have. Those numbers mean that $600 of the credit can only go toward reducing tax owed, which you won't have any of if you have no income. But $1400 can be claimed even if you owed $0 in taxes.
The Earned Income Tax Credit is another refundable credit you may be able to claim if you had a small amount of earned income, though not if you had none. The amount of that credit depends on your situation.
In summary, if you had no income or very little income in 2019, you are not required to file a tax return. But you may do so if you want and would likely receive some money as a result of doing so.