Ganga, Jamuna and Saraswati, the trio Sangam in Allahabad, is believed to be the holiest place in the country where taking a dip can wash away all past sins. After death, ashes are also submerged in Ganga water with an assumption that the past sins will be removed.

In Vedic era, what was the intention of the rishis and munis while making this ritual?

In mythology, moon represents cool mind and Ganga represents the positive flow of thoughts. And sea turmoil indicates the disturbed state of mind. Hanuman ki samudra yatra indicates the meditative journey through the flow of thoughts. Samudra manthan represents the journey of the mind during meditation.

Taking a dip can be equated to shifting your mind towards your consciousness, which can happen when you introspect in a relaxed state of mind or when you practice meditation. Meditation is defined as a journey from sympathetic to parasympathetic state of mind or a journey from disturbed state of consciousness to undisturbed state of consciousness. Every time you meditate, you dip into your consciousness and clean your guilt and negative thoughts. It is something like reformatting your hard disk and removing the bad sectors and viruses in your software. It is, therefore, possible for you to do Ganga snan (bath) at your house in the morning while meditating or during pooja by drifting away from disturbed state of mind to non-disturbed relaxed state of mind, clearing your guilt and negative thoughts.