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Is osmand normally terrible?
(suppo.fi)
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What you're describing sounds like an issue with either A-GPS (a mechanism by which sat navs can receive initial data over a cellphone connection, without which the initial location search can last up to 10 minutes, but afterwards it will be as smooth as always) or approximate location (a mechanism in which Google uses a huge database of cell tower and Wi-Fi data to quickly get your approximate position).
I would suggest checking the permissions on the OSMAnd app -- maybe it's lacking something that Google Maps has?