My Verified Google My Business Profile place marker doesn’t show by default unless I search for it. I want to see the label of my business without searching for it.

Unfortunately, not every business can be represented on the map when you look at an area, and not desirable as in many locations, e.g. downtowns, you probably wouldn’t see the Map itself.

Google’s statement in relation to place labels:
“Place labels are a feature of Google Maps that surfaces great content such as landmarks, businesses, and tourist attractions on Google’s base map data.
The place labels shown on Google Maps are determined algorithmically based on a large number of factors. One factor these algorithms consider is the accuracy of the business information and the richness of the content associated with the business. “

In other words, for your Google (My) Business Profile to appear on the map without searching for it, you need to:

First

Engage with your profile: complete it in full, respond to comments, keep posting, add promotions, photos, etc.

Because these tasks will help your customers engage with your business, and Google likes it, therefore you will have better chances for your business place label to appear.

Second 

Improve your listing ranking by studying the Google Local Ranking Algorithms Factors and implementing strategies for that effect. Google advises the following:

Relevance

Relevance refers to how well a local Business Profile matches what someone is searching for. Add complete and detailed business information to help Google better understand your business and match your profile to relevant searches.

Distance

Distance considers how far each potential search result is from the location term used in a search. If a user doesn’t specify a location in their search, the distance calculation is based on what we do know about their location.

Prominence

Prominence refers to how well-known a business is. Some places are more prominent in the offline world, and search results try to reflect this in local ranking. For example, famous museums, landmark hotels, or well-known store brands are also likely to be prominent in local search results.