For proof of the LOA you could also manifest something improbable, rather than something big. I'm a numbers person so something highly improbably can get my attention easily, and infact I'm to cerebral to have been willing to take much in the way of risks.
I'm a video gamer, so I set an intention for an exchange of data from another player the next day, I would have been happy with any exchange that was international but I picked out the country I wanted that trade to happen with expecting it to be from anywhere but there the moment I thought about it, and since I had thought of the next day I had assumed it would be several days because the peice of data I was offering up in trade wasn't valuable within the game, they could have gotten in from just about any gamer in this country.
The next day I found out I had exchanged the data with a person from the country I had originally decided upon. That was so improbable that I took it as proof of the LOA when that happened (it was just to improbable for me to ignore). It was perfect, low risk action, highly improbable outcome, and on top of that another person was invloved in the exchage of data, that didn't just make me an LOA beleiver it, the nature of that exchange mirrored the way goods and services are exchanged on the internet between business owners and customers was so closely mirrored that I consider that exchange of data one of my primary inspirations for deciding to start my own business.