The conventional room geometry blind inference techniques with acoustic signals are conducted based on the prior knowledge of the environment, such as the room impulse response (RIR) or the sound source position, which will limit its application under unknown scenarios. To solve this problem, we have proposed a room geometry reconstruction method in this paper by using the geometric relation between the direct signal and first-order reflections. In addition to the information of the compact microphone array itself, this method does not need any precognition of the environmental parameters. Besides, the learning-based DNN models are designed and used to improve the accuracy and integrity of the localization results of the direct source and first-order reflections. The direction of arrival (DOA) and time difference of arrival (TDOA) information of the direct and reflected signals are firstly estimated using the proposed DCNN and TD-CNN models, which have higher sensitivity and accuracy than the conventional methods. Then the position of the sound source is inferred by integrating the DOA, TDOA and array height using the proposed DNN model. After that, the positions of image sources and corresponding boundaries are derived based on the geometric relation. Experimental results of both simulations and real measurements verify the effectiveness and accuracy of the proposed techniques compared with the conventional methods under different reverberant environments.