Professor Paul A. Moody of the University of Vermont suggests large floating land masses could have transported them:

In times of flood, large masses of earth and entwining vegetation, including trees, may be torn loose from banks of rivers, and swept out to sea. Sometimes such masses are encountered floating in the ocean out of sight of land, still lush and green, with palms twenty to thirty feet tall. It is entirely probable that land animals may be transported long distances in this manner. Mayr records that many tropical ocean currents have a speed of at least two knots; this would amount to fifty miles in a day, 1,000 miles in three weeks. (Introduction to Evolution, p. 262)

Frank L. Marsh argues that the migration can be validated by connected land masses which existed at one time.

One glance at a world map will show that, with the exception of the narrow break at the Bering Strait, a dry-land path leads from Armenia to all lands of the globe except Australia. In the case of the latter [Australia] the East Indies even today form a fairly continuous bridge of steppingstones to that southern continent. As regards [p. 1197] the Bering Strait, there is no doubt that a land connection once existed between Asia and North America. (Evolution, Creation, and Science, pp. 291–292)