Accurate initialization is essential for reliable visual-inertial odometry (VIO), but it is often ill-conditioned under degenerate motions. Existing methods typically require restrictive excitation motions to ensure sufficient observability or rely on computationally expensive 3D structure reconstruction, limiting efficient and practical deployment. To address these limitations, we propose SLIM-init, a structureless monocular VIO initializer that directly exploits geometric constraints from tracked 2D line features without explicit 3D landmark reconstruction. Specifically, SLIM-init leverages line-derived vanishing points (VPs) as translation-invariant orientation cues to provide robust rotation-only constraints under degenerate scenarios such as low-parallax or translation-dominant motions. It further incorporates a line epipolar residual to constrain translation and a line-normal projection residual to improve the conditioning of linear alignment, enhancing the accuracy and robustness of initial state estimation. Extensive experiments on a public benchmark and challenging custom degenerate-motion sequences demonstrate improved accuracy and robustness over state-of-the-art initialization methods. The source code is available at: https://github.com/cjunwan/SLIM-init.

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