This study numerically investigated spontaneous ignition in the middle of a vertically placed solid thin fuel heated by external radiation in a normal-gravity quiescent environment. The ambient oxygen mass fraction varied from 35% down to the nonignition limit. Numerical results indicate that, in the nonignition case, the maximum reaction rate and maximum temperature in the gas phase were too weak to achieve the combustion reaction. For ambient oxygen mass fraction exceeding 17%, the ignition and transition to flame spread are all achievable. The ignited flame lengthens and strengthens with decreasing ambient oxygen mass fraction. The rate of flame growth was found to exceed that of the purely opposed and purely concurrent spread flames. Although the ignited flame is smaller, the propagating flame in high ambient oxygen mass fraction becomes longer and stronger in structure than the low-oxygen flame after 2 s of flame growth time. Our results further demonstrate that the flame growth rate in transition increases with the mass fraction of ambient oxygen.