Do a start-up should search for angel financing between seed and round A even if it's burn rate is low and have a budget to operate till round A?

Raising money is a choice, if you can self funded until the concept is proven and you start getting traction, don't give up equity early on. In any round, you give up a piece of the pie, the longer you are able to self fund, the better the end result for you.
You will be in strong position if you are able to stay out of asking for funding early on, but remember you need to have a good hold of the market and your numbers to understand when

My personal rule is... I only start businesses that self fund easily.

If I can turn an idea into a first sale, by end of day, I figure the idea is of little value.

If you can turn ideas into profit rapidly, with zero investment, then your business will succeed well.

You might find it good to hire someone to walk through your business with you + figure out how to simply refine your current business model to produce high profits.

This will instantly fund your business, so you can stop pitching + start profiting.

Do a bridge round only if you need the funds for critical operations. If you can postpone it or manage till A then avoid it, so that you get best valuation and retain more equity.