How to decide a budget?

In Scrum the basic unit of accounting is the Sprint. How much does it cost to fund X teams for Y Sprints?

The more Sprints purchased, the more innovation runway there is for learning to build the right thing at the right time.

Do you know how much the idea is worth to you? If so, that's a good starting point. If the feature is worth $X, you probably don't want to spend more than $X to build it. You probably don't want to spend exactly $X. Instead, you want to spend some fraction of $X. You just need to know how big of a fraction you're willing to spend, at most, to learn if your idea has merit.

Once you know how much you're willing to spend, you need to fund a team. If you have an existing team of a Scrum Master, Product Owner, and Developers, then you should know how much they cost per unit of time (ideally in weeks, months, or Sprints). Since you know the maximum you're willing to spend and the cost for a team, you can figure out how many weeks, months, or Sprints you can afford and then check to see if you are likely to get something valuable within that upper limit of time. If you don't have an existing team, you can use your budget to buy a team.