Edge Gaussian splatting (EGS), which aggregates data from distributed clients (e.g., drones) and trains a global GS model at the edge (e.g., ground server), is an emerging paradigm for scene reconstruction in low-altitude economy. Unlike traditional edge resource management methods that emphasize communication throughput or general-purpose learning performance, EGS explicitly aims to maximize the GS qualities, rendering existing approaches inapplicable. To address this problem, this paper formulates a novel GS-oriented objective function that distinguishes the heterogeneous view contributions of different clients. However, evaluating this function in turn requires clients' images, leading to a causality dilemma. To this end, this paper further proposes a sample-then-transmit EGS (or STT-GS for short) strategy, which first samples a subset of images as pilot data from each client for loss prediction. Based on the first-stage evaluation, communication resources are then prioritized towards more valuable clients. To achieve efficient sampling, a feature-domain clustering (FDC) scheme is proposed to select the most representative data and pilot transmission time minimization (PTTM) is adopted to reduce the pilot overhead. Subsequently, we develop a joint client selection and power control (JCSPC) framework to maximize the GS-oriented function under communication resource constraints. Despite the nonconvexity of the problem, we propose a low-complexity efficient solution based on the penalty alternating majorization minimization (PAMM) algorithm. Experiments reveal that the proposed scheme significantly outperforms existing benchmarks on real-world datasets. The GS-oriented objective can be accurately predicted with low sampling ratios (e.g., 10%), and our method achieves an excellent tradeoff between view contributions and communication costs.