Yes, you can get a pre paid 60 day tourist visa that you apply for from overseas - but it is not renewable like a 6mth social budaya visa is (ie; Social Budaya Visa gets you an initial 2 mths + 4x1 mth permissible extensions)

Otherwise there is a paid tourist visa on arrival which is renewable for 1 month only .., otherwise there is a free visa on arrival but note; that one is not renewable.

I was living here in Indonesia on a sponsored (6mth) Social budaya visa for my 1st 2 years living in Indonesia .., ie; until I eventually qualified for a kitas visa , then onto kitap visa (ie; permanent resident visa).

Travellers can arrive in Indonesia on any tourist visa ...., then while here they could apply at a visa agent for a 6 month social budaya (who for a price will act as a sponsor). The visa agent will then give you the completed necessary forms to which you will fly out to Singapore for a day(for eg) and submit the paperwork, and then fly back on the social budaya visa.

This is actually illegal for the agents to sponsor you as the contact with you is a business transaction and not 'a bonafide social visit' as would be between friends and family etc.., and this is part of the reason for the high price they charge for their service, as some of that money you pay to them also goes toward the agents greasing a few palms at the immigration dept to process the agents paperwork.
Occasionally there is a crackdown on these agents, but it never lasts to long before it goes back to their old ways