We consider avalanche photodiodes (APDs) functioning under near Geiger-mode operation for extremely weak light (single or several photons) detection, such as in LiDAR receivers. To meet such demands, APDs which simultaneously have a large active window size, moderate bandwidth (∼GHz), and high internal gain (responsivity), are highly desired. However, it is difficult to design APDs capable of meeting the afore-mentioned performance requirements due to the intrinsic limitations of the gain-bandwidth product (GBP). In this work, we demonstrate that the GBP bottleneck in the APDs can be overcome by using multiple (3) In0.52Al0.48As based multiplication (M-) layers with a thick In0.53Ga0.47As absorber (2 µm). Moreover, the characteristic invariant 3-dB bandwidth in our APDs, from low to an extremely high operation gain, becomes more pronounced with an increase of its active window diameter (40 to 200 µm). This characteristic makes it very attractive for collecting weak light in free space as is required for LIDAR receiver applications. Comparison shows that the 200 µm APD exhibits a higher 0.9 Vbr responsivity (15 vs. 7 A/W), larger maximum gain (460 vs. 110), and higher GBP (468 vs. 131 GHz) than does the 40 µm reference sample and can sustain a constant 3-dB bandwidth (1.4 GHz) over a wide range of operation gains (10 to 460). The dependence of the APD performance on the window size can be attributed to the influence of the surface states on the edge of the etched mesa. Here, we further demonstrate a backside-illuminated structure with a flip-chip bonding package which minimizes this phenomenon in small APDs ensuring high-speed performance. Compared with the top-illuminated reference samples, the flip-chip bonding packaged device shows a further enhancement of the responsivity (10.7 vs. 7 A/W), 3-dB bandwidth (4.1 vs. 3.9 GHz), and saturation current (4.25 vs. 3.6 mA). The excellent static and dynamic performance of our flip-chip APD in turn leads to an unprecedented high velocity sensitivity (5 µm/sec) and superior quality 4-D FMCW LiDAR images compared to that obtainable with p-i-n-based or top-illuminated reference devices with the same small active window size (40 µm).