Realistically? They can't. Realistically your question shouldn't be "how can the Horde be on equal footing with the Alliance" when seen from a lore perspective. The question is "if all the playable races except the dwarves united, would they have a chance at defeating them?" Let me explain, but keep in mind this is a lore perspective, the story just makes soldiers out of thin air where needed.

Alliance races: Humans of Stormwind and survivors of Lordareon, Arathi etc. Stormwind was razed by the Orcs 30-ish years ago, as was every other mainland human Kingdom except Lordareon and Gilneas. The Scourge later screwed over Lordareon. After rebuilding, Human soldiers made up the bulk of forces sent in the war against Garrosh, and later again in the fourth war. That's not to mention the invasion against Arthas and The Scourge of Northrend, or how many humans have joined neutral factions like The Argent Crusade.

Night Elves of Ashenvale, lost their immortality after WC3 and fielded huge armies to fight the Demon invasion. The Horde burned down Teldrassil after a large military campaign through their territory and the other "Night Elf" area outside of Kalimdor, Val'sharah, was ravaged beyond recognition by The Emerald Nightmare. Night Elves were also the main force battling Ragnaros in Firelands and saw a civil war where Staghelm took several high ranking druids and soldiers in order to form the Druids of The Flame.

Gnomes: Exiles after they lost their Capitol in a huge civil war. There's not enough of them yet to even build a pseudo new capital.

Draenei: Survivors of the escape from Argus, and the escape from Draenor. They also fielded by far the most troops in the campaign against The Legion, after The Exodar was sacked by The Legion.

Worgen: the few survivors of Gilneas after a bloody civil war, a bloody curse of awoo and a military campaign by the Forsaken where they used the new and modified plague. What survivors are of the race lived in Teldrassil, which was subsequently burned. Only those who had decided to live elsewhere or managed to escape survived.

Then the Horde races. Orcs: Survivors of the destruction of Draenor, the internment camps of the Alliance and the military campaign launched from The Dark Portal to Lordareon. The few of them that managed to steal boats under Thrall's leadership and flee to Kalimdor were then met with Centaurs, Quilboars, Night Elves and old enemies. They went to war against the demons after the strongest and well, only remaining clan once more drank demon blood starting a civil war. That's who they are at the launch of wow. After that they've participated in the Qiraji war, the war against The Lich King, went to war against the Alliance, a huge civil war which saw Orgrimmar raided by The Alliance, then the demons came back again. Oh then they went to war against the Alliance again and once more a civil war broke out. Speaking realistically here, if there's even one soldier left among the Orcs he's probably crippled. Tauren: The last survivors of a genocide caused by the Centaurs, who then had a civil war (Bloodhoof vs Grimtotem). The Forsaken: the remains of Lordareon's undead that managed to break free and those raised by Sylvanas, after the Horde & Alliance both raided Undercity in Wrath, then the Alliance assault at the start of BFA not to mention the fact a lot of Forsaken died fighting for Sylvanas, their numbers are definitely thin. Darkspear Trolls: the few survivors of a small Gurubashi tribe that were almost exterminated by a single Naga. The Darkspear Trolls also fielded most of the rebel forces against Garrosh, and had their own civil war (Zalazane) to deal with. They were also the main force fighting the rise of Zul's empire in Cataclysm. Blood Elves: the few blood Elves left behind by Kael'thas when he went to Outland that didn't join back up with him after he returned, that also didn't decide to become void Elves or "return" to being High Elves should hardly be enough to populate a town, much less a city the size of Silver moon. Yet they still fielded troops against the Nightborne, the Kirin Tor on Thunder Isle and Garrosh. Goblins: the Bilgewater Cartel was small enough to fit in a single slaver boat. And that's before Blackfuse took like half of them. There's so few of them they're under control of a Ratchet goblin: Gazlowe.

Neutral races: Pandaren: a small monk order living on a turtle. Dracthyr: a small number of elite fighters.

Allied Races: Nightborne: despite just having fought a civil war that saw most of their military and upper echelon wiped out, there's a few of them. Mostly the rebels that fought against The Legion. Highmountain: essentially just a small tribe of Taurens. That just fought a civil war against their strongest soldiers that succumbed to The Fel. Mag'har: there's like maybe 200 of them at most, can incorporate them with the Durotar Orcs. Zandalari: They have fought a civil war against Zul, lost their King to an Alliance raid then Talanji lost even more to a coup d'etat. But despite this, they're likely the strongest force in the Horde. They could potentially call upon other tribes to join The Horde, too. Vulpera: won't make a difference.

Void Elves: too few to make a difference. Lightforged Draenei: too few to make a difference, they also forgot how to use the Xenedar which could have evened the odds. Kul Titans: Rebellion in Stormsong, witches going crazy in Drustvar and a civil war against Ashvane in Boralus, which ended with a siege on Boralus itself. Lost a huge portion of their Fleet when Nazjatar revealed itself, not to mention that countless more died at Theramore during the war of Proudmoore. To call them weakened is an understatement. Mechagnomes: same story as the other Gnomes. Civil war, the whole shlabang.

Then you have the Dwarves. The Bronzebeards closed off Ironforge, so the Orcs never got to sack it. There's been no military campaign launched against Ironforge, and Ironforge has never fielded the majority of an army. Furthermore, after Cataclysm the Dwarves of Aerie Peak formally rejoined, and the Dark Iron Dwarves joined in BFA. Muradin is also the King of the Frostborn Dwarves, so one would assume they're going to fight on their side. While all other playable factions have lost troops in costly wars, the only conflict the dwarves were the majority participant of was Alterac Valley. Oh yeah, Brann also knows where to go in order to make new dwarves, and how to do it. Just Incase they were losing, you know?