Unsupervised learning can be a good starting point. You can do a clustering (k-means/hierarchical) of existing user-base to find patterns in it (example: cluster 1 contains employees with Windows laptop with 4 GB RAM and photoshop pre-installed , cluster 2 is Mac with 16 GB memory). Then for a new employee, predict the nearest matching cluster and use the pre-dominant setup of that cluster.
The problem is there may be lot of lot of variation in the same cluster, especially on softwares installed.
Other alternative is to convert it to a supervised learning problem with hand-rolled categories as outcome (example: 'laptops with lot of RAM and graphics software', 'laptops for development') and then predict that category. You will need upfront work and domain knowledge to create the categories. But it will reduce the predicted variable space by a large margin.
But How to Create Categories?
Maths can help us a little bit here. Let us assume that you have an N dimensional one-hot encoded vector representing the hardware and software setup. Let us make the assumption that there are a handful of latent K categories of the setup encoded by a large dimensional vector of size N. To go about finding those, you can take a low dimensional projection of the encoding vector. This is probably a mathematical way of finding the categories instead of what you'd do manually on the output of clustering/unsupervised approach.
Radical Alternative: Recommendations
If you have enough data, you can pose it as 'recommending right setup to a new employee' problem. Take any standard movie recommendation kind of setting with users and movie ratings. Replace users -> employees and movies with a unique hardware + software setup. Use standard recommendation algorithm applied to binary data.
All these approaches are actually variant of low dimensional projection of the encoding vector + similarity calculation with existing users.
Hope this helps.