The uncertainty of successful ignition in non-premixed turbulent flows remains a fundamental challenge in many practical combustion systems. Mapping the spatial distribution of ignition probability often relies on iterative testing that becomes prohibitive when measuring sensitivity to a large number of parameters or varied flow conditions. An accelerated approach is to formulate the adjoint of the perturbed and linearized governing equations in such a way that sensitivity of an ignition indictor to an arbitrarily large number of parameters can be obtained with a cost comparable to the flow solution. The purpose of the present study is to demonstrate the capability of an adjoint solution to inform parametric uncertainty and optimal ignition placement in turbulent non-premixed combustion. Direct numerical simulations of assisted ignition in a non-premixed hydrogen-air mixing layer are presented. Adjoint-based sensitivity of ignition likelihood to placement of the igniter are reported for different flow realizations.