Of course it is possible. But will the game be any good or playable. Or will peolpe be willing to pay for it. The company behind the newer Sherlock games has 80+ employess and pumps out about 1 game a year. And this is with expericence...
The hardest part for such a game is writing. I am told some authors even get away with only writing the story and selling it printed on paper, no engine whatsoever :-b
I am missing the position of writer in your list above. And for your deduction stuff you need not only game mechanic, but elevate the story to a playable experience. Otherwise you need a lot of bells and whistles to sell a walking simulator. Also you have no quality assurance /game testing planned.
But from a pure mechanical viewpoint, sure, clobber a prototype with bland assets and maps in a ready to go engine and make it pretty afterwards. Assuming you do have a story. That should give you quite an insight how much work there might be involved. The first few puzzles should do .
For your guesswork, you can do what i did. Just look at released games and their companies. How much people work there, how many gams do they realease. Or look at kickstarter projects . How much took successful games to fund their game. You can calculate back, how many dev hours you could pay with that.