How to handle 30-day notice requirement for court marriage?

Hi, my sister is getting married in December this year. We’re living in the UK, and the groom is from the United States. The bride and groom would like to get a court marriage done before the actual wedding in December, ideally at the start of November, so that they can apply for a dependent visa (for the USA) and travel immediately after the wedding. However, when we looked online, it says that the marriage must be declared 30 days in advance before the registrar can approve it. What can we do in this situation? Do they have to go to India at the start of October to register, or can it be done by our parents on their behalf so that they can travel once the registrar accepts and provides a date for the court marriage?