Anthem offers multiple suits with the Javelins that function like different classes. One of the four suits will likely be an option for actual melee combat.
So far, Anthem has mainly shown combat at medium ranges, but there will likely be more options. Depending on the Javelin and equipment, you can influence your playstyle. Bioware now confirms that melee builds are also possible.
What are Javelins? These are the combat suits that you wear in Anthem. They have different skills, weapons, and gear, and function similarly to classes in RPGs.

Each Javelin will also have a super attack, of which this information is currently known.
In response to increased fan inquiries, Ben Irving, the lead producer of Anthem, has confirmed that there will also be melee gear for the Interceptor Javelin. There will, however, be no stealth.
Anthem lets you fight at close range, but not stealthily
This Javelin suit supports melee combat: According to Irving, they have already planned gear for the Interceptor that allows for a melee build.
We decided to create gear for the Interceptor that allows for a melee build (perhaps more).
What distinguishes the Interceptor? This suit is the smallest and fastest Javelin in Anthem. According to EA, it is popular with scouts and assassins.
Apparently, it has some evasion abilities and can equip any (non-heavy) weapon. By default, the Interceptor is equipped with dual-sided daggers and a melee skill.

The playstyle is likely to charge into the ranks of enemies with the speed of the Interceptor, deal damage, and then retreat. However, there will be no stealth capabilities.
Is new gameplay coming soon? So far, there is no gameplay of a melee build. However, that could change soon, as EA may plan to release new material shortly. Something along those lines was announced by Bioware on Reddit.
Although the team is working hard on the game […], that does not mean we won’t have something to show soon.
The word “soon” is indeed a cliché here, they are aware of that, but there is currently nothing more to say. Recently, Anthem reached alpha status.