This would typically be improper and you would be entitled to payment for the hours worked if you were required to be present at the time you arrived. Each state has slightly different laws but I have had employers change time cards and it typically comes back to haunt them. Speak with a local attorney about all of the facts and see what rights you may have in this regard. From the limited facts you provide, you might have a viable legal claim.
The answer to your question (like many questions in employment law) is not entirely straight-forward. The starting point is that the employer is obligated to maintain accurate records of the time its employees work. It is, therefore, permissible for an employer to change time cards IF the change accurately reflects the time the employee actually worked.
So, the next question is if the time between your arrival and the time the first child shows up is considered time worked.
If you have absolutely no work obligations during this time before the first child arrives, and you are completely free to attend to personal matters (including going around the corner to get a cup of coffee from the local coffee shop), then the employer has an argument that you are not yet working and, therefore, has no oblgation to pay you. Alternatively, if you have any work restrictions placed up you (e.g., you need to straighten up, get projects ready, or you cannot leave to go get that cup of coffee), then you are considered "on the clock" and the employer has to pay you for that time.