Laser welding processes are highly sensitive to the alignment of the laser beam with respect to the joint location. Even minor deviations—referred to as beam offsets can induce critical defects in the final weld. This issue is particularly pronounced in stake welding of hidden T-joints, where the joint interface is not accessible from the top surface, rendering conventional vision-based seam tracking methods ineffective. To address this challenge, this study proposes a computer vision-based system employing LED illumination to acquire real-time images of the melt pool for early detection of beam offsets. The underlying hypothesis is that variations in melt pool geometry are indicative of beam misalignment; however, this relationship is complex and non-linear, necessitating a data-driven approach. A convolutional neural network is developed and trained to classify melt pool images into categories representing correct alignment and beam offset conditions. Experimental validation is conducted using image datasets obtained from controlled laser welding trials. The proposed method demonstrates high classification accuracy and holds significant potential for in-process quality assurance and defect prevention in laser stake welding of T-joints.