Hi,
Topology is important to make sure that your lines are connected properly. If you are sure of the connections of lines or if you are sure of the quality of the source from where you have the shapefiles or feature class, then you can skip topology. You can proceed to defining connectivity 🙂
If you do not have any attributes, just start with shape_length so that your solution is based on shortest distance. You can easily convert the distance to speed by diving it by average speed of the mode. For example, if it is a walking network, just use the speed between 3 to 4 km/hr, if bicycle take 10-15km/hr. So time taken = (distance/ speed). Then you can use the same procedures for shortest time.
regards,