How do you increase profitability of your organization and engage in continuous improvement to be more competitive?

I think you should start to focus on improvement projects that aims for cost saving or increased productivity, and try to do it with minimum or no cost and risk.  For example: power/water saving or new method that saves raw material.  Therefore, you can show the increased profit/reduced cost to your management in a more direct manner.

Other projects that aims for increased safety and quality may in the long run give even more savings and profit.  However, it may not be as straightforward and may need cost and have more risk of failure.  So I suppose you may need to prove yourself first.