  This paper presents a novel approach to establish a blow-up mechanism for the
forced 3D incompressible Euler equations, with a specific focus on
non-axisymmetric solutions. We construct solutions on $\mathbb{R}^3$ within the
function space $C^{3,\frac12}\cap L^2$ for the time interval $[0, T)$, where $T
> 0$ is finite, subject to a uniform force in $C^{1,\frac12 -\epsilon}\cap
L^2$. Remarkably, our methodology results in a blow-up: as the time $t$
approaches the blow-up moment $T$, the integral $\int_0^t |\nabla u| ds$ tends
to infinity, all while preserving the solution's smoothness throughout, except
at the origin. In the process of our blow-up construction, self-similar
coordinates are not utilized and we are able to treat solutions beyond the
$C^{1,\frac13+}$ threshold regularity of axy-symmetric solutions without swirl.
