Use of 'The' at the beginning of a sentence

Question

1. The payment was made today
2. Payment was made today

In which context, the above can be used.

Answer 1

Is the question "which payment?" important?

If yes, use the article. You're expecting the listener/reader to know which payment. If you don't think the listener/reader will assume correctly you will have to add more words to the sentence.

If not, no article needed or you can use the indefinite article.