Spatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number-space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading and writing. However, some early forms of a number-space link have been observed in preschool children who cannot yet read and write. As literacy experience is evidently not necessary for number-space effects, we are searching for other potential sources of this association. Here we propose and test a hypothesis that the number-space link can be quickly constructed in preschool children's cognition on the basis of spatially oriented visuo-motor activities. We trained 3- and 4-year-old children with a non-numerical spatial movement task (left-to-right or right-to-left), where via touch screen children had to move a frog across a pond. After the training, children had to perform a numerosity comparison task. After left-to-right training, we observed a SNARC-like effect (reactions to smaller numbers were faster on the left side, and reactions to larger numbers on the right side), and after right-to-left training a reverse effect. These results are the first to show a causal link between visuo-motor activities and number-space associations in children before they learn to read and write. We argue that simple activities, such as manual games, dominant in a given society, might shape number-space associations in children in a way similar to lifelong reading training.