A booth is not the only possibility
Booths are great! They are an area dedicated wholly to the sponsoring company, which offers great flexibility. It provides a gathering point where attendees can seek you out at the event, and it provides a spot where you can direct people to find your company.
Booths are also not the only option. Sponsorship decks or one-sheeters are just the ideas the event planners thought most widely accessible. They may have had to trim offerings to keep it from sprawling, or there may be sponsorable areas that they just didn’t think of to offer. Any sponsoring company has the ability to offer to make their activation any part of the event — and most event planners will go for it, so long as it doesn’t conflict with any other package or impinge the attendee experience.
For example, you are a jogging shoe brand that wants to sponsor an outdoor weekend street festival in the middle of August. One creative idea that would connect the shoes with people who walk their dogs regularly is to sponsor puppy hydration stations or shade areas. The lift is relatively light — simply put out bowls of water (get them custom-made to look like the brand’s dog walking shoes) at pre-determined locations (ask about getting these on the event map) and signage. Periodically throughout the event refill bowls — the event planners may even be willing to help with this.
This achieves several things:
Reducing the staffing expense to work a booth
Organic integration to the event, one that makes people seek out your marketing to them
Gratitude from the event planners - your activation betters the attendee experience, and the planners are now more likely to be flexible with you in the future with out-of-the-box ideas
Associations between the brand and: happy feelings (gratitude + fun), their dogs, being outdoors, & activity / movement
Memorability
This was likely not on the standard sponsorship deck, but that doesn’t mean it’s not available. Creativity here can win the day!