Motion-to is expressed by the verb.
The goal is marked by the all-purpose prepositon na which is neutral with regard to 'motion(-to/from)' vs. 'position-at', plus ini 'in(side)'; na ini may be preceded by te 'until'.
We did not find any clear instances of na used without ini 'in(side) in this context in the 18th-century sources.
Even though there are no examples with 'push into' in the available sources, a serial verb construction plus preposition appears with other meanings. It was probably a possibility with 'push into' as well. The example provided for 'push into' is a constructed one.
Source: Schumann 1781: 163
Source: van Dyk ca. 1765: 76
Source: Schumann 1781: 58
Source: Schumann 1783: 83