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Obiously there cannot be a straight numerical answer to our questions, as the time to success largely depends on your current skills and the time you can invest.

I suggest you spend a day or an afternoon doing the core ROS tutorials, and other tutorials that seem of interest to you, like mapping and navigation tutorials. After that day you should be able to judge yourself how much time you can expect to require.

However you could also ask another question where yo give more details on the hardware specs of your target DIY platform and sensor, to find people working on similar platforms who can share tips or code with you.