diff --git a/geometry/meshcat_visualizer.cc b/geometry/meshcat_visualizer.cc
index 66d7df8582c0..51a2e68971be 100644
--- a/geometry/meshcat_visualizer.cc
+++ b/geometry/meshcat_visualizer.cc
@@ -49,8 +49,6 @@ MeshcatVisualizer<T>::MeshcatVisualizer(std::shared_ptr<Meshcat> meshcat,
       this->DeclareAbstractInputPort("query_object", Value<QueryObject<T>>())
           .get_index();
 
-  meshcat_->SetProperty(params_.prefix, "visible", params_.visible_by_default);
-
   if (params_.enable_alpha_slider) {
     meshcat_->AddSlider(
       alpha_slider_name_, 0.02, 1.0, 0.02, alpha_value_);
@@ -65,7 +63,7 @@ MeshcatVisualizer<T>::MeshcatVisualizer(const MeshcatVisualizer<U>& other)
 template <typename T>
 void MeshcatVisualizer<T>::Delete() const {
   meshcat_->Delete(params_.prefix);
-  version_ = GeometryVersion();
+  version_ = std::nullopt;
 }
 
 template <typename T>
@@ -127,8 +125,15 @@ systems::EventStatus MeshcatVisualizer<T>::UpdateMeshcat(
       query_object_input_port().template Eval<QueryObject<T>>(context);
   const GeometryVersion& current_version =
       query_object.inspector().geometry_version();
-
-  if (!version_.IsSameAs(current_version, params_.role)) {
+  if (!version_.has_value()) {
+    // When our current version is null, that means we haven't added any
+    // geometry to Meshcat yet, which means we also need to establish our
+    // default visibility just prior to sending the geometry.
+    meshcat_->SetProperty(params_.prefix, "visible",
+                          params_.visible_by_default);
+  }
+  if (!version_.has_value() ||
+      !version_->IsSameAs(current_version, params_.role)) {
     SetObjects(query_object.inspector());
     version_ = current_version;
   }
@@ -281,7 +286,6 @@ template <typename T>
 systems::EventStatus MeshcatVisualizer<T>::OnInitialization(
     const systems::Context<T>&) const {
   Delete();
-  meshcat_->SetProperty(params_.prefix, "visible", params_.visible_by_default);
   return systems::EventStatus::Succeeded();
 }
 
diff --git a/geometry/meshcat_visualizer.h b/geometry/meshcat_visualizer.h
index 3a24db06e60f..c757b0c6eda3 100644
--- a/geometry/meshcat_visualizer.h
+++ b/geometry/meshcat_visualizer.h
@@ -2,6 +2,7 @@
 
 #include <map>
 #include <memory>
+#include <optional>
 #include <string>
 
 #include "drake/geometry/geometry_roles.h"
@@ -193,7 +194,7 @@ class MeshcatVisualizer final : public systems::LeafSystem<T> {
    before SetTransforms. This is intended to track the information in meshcat_,
    and is therefore also a mutable member variable (instead of declared state).
    */
-  mutable GeometryVersion version_;
+  mutable std::optional<GeometryVersion> version_;
 
   /* A store of the dynamic frames and their path. It is coupled with the
    version_.  This is only for efficiency; it does not represent undeclared
diff --git a/geometry/test/meshcat_visualizer_test.cc b/geometry/test/meshcat_visualizer_test.cc
index 00745ad73862..4f75b6cc0c00 100644
--- a/geometry/test/meshcat_visualizer_test.cc
+++ b/geometry/test/meshcat_visualizer_test.cc
@@ -66,6 +66,7 @@ class MeshcatVisualizerWithIiwaTest : public ::testing::Test {
     ASSERT_TRUE(meshcat_->HasPath(path));
     const std::string property =
         meshcat_->GetPackedProperty(path, "visible");
+    ASSERT_GT(property.size(), 0);
     msgpack::object_handle oh =
         msgpack::unpack(property.data(), property.size());
     auto data = oh.get().as<internal::SetPropertyData<bool>>();
@@ -84,6 +85,10 @@ class MeshcatVisualizerWithIiwaTest : public ::testing::Test {
 TEST_F(MeshcatVisualizerWithIiwaTest, BasicTest) {
   SetUpDiagram();
 
+  // Visibility remains unset until geometry gets added.
+  EXPECT_EQ(meshcat_->GetPackedProperty("/drake/visualizer", "visible").size(),
+            0);
+
   EXPECT_FALSE(meshcat_->HasPath("/drake/visualizer/iiwa14"));
   diagram_->ForcedPublish(*context_);
   EXPECT_TRUE(meshcat_->HasPath("/drake/visualizer/iiwa14"));
@@ -92,6 +97,7 @@ TEST_F(MeshcatVisualizerWithIiwaTest, BasicTest) {
                   fmt::format("/drake/visualizer/iiwa14/iiwa_link_{}", link)),
               "");
   }
+  CheckVisible("/drake/visualizer", true);
 
   // Confirm that the transforms change after running a simulation.
   const std::string packed_X_W7 =
@@ -100,8 +106,6 @@ TEST_F(MeshcatVisualizerWithIiwaTest, BasicTest) {
   simulator.AdvanceTo(0.1);
   EXPECT_NE(meshcat_->GetPackedTransform("visualizer/iiwa14/iiwa_link_7"),
             packed_X_W7);
-
-  CheckVisible("/drake/visualizer", true);
 }
 
 TEST_F(MeshcatVisualizerWithIiwaTest, PublishPeriod) {
@@ -179,8 +183,10 @@ TEST_F(MeshcatVisualizerWithIiwaTest, NotVisibleByDefault) {
   MeshcatVisualizerParams params;
   params.visible_by_default = false;
 
-  // Create the diagram and publish both the initialization and periodic event.
+  // Create and run the diagram.
   SetUpDiagram(params);
+  systems::Simulator<double> simulator(*diagram_);
+  simulator.AdvanceTo(0.1);
 
   // Confirm that the path was added but was set to be invisible.
   CheckVisible("/drake/visualizer", false);
@@ -189,7 +195,6 @@ TEST_F(MeshcatVisualizerWithIiwaTest, NotVisibleByDefault) {
 TEST_F(MeshcatVisualizerWithIiwaTest, DeletePrefixOnInitialization) {
   MeshcatVisualizerParams params;
   params.delete_on_initialization_event = true;
-  params.visible_by_default = false;
   SetUpDiagram(params);
   // Scribble a transform onto the scene tree beneath the visualizer prefix.
   meshcat_->SetTransform("/drake/visualizer/my_random_path",
@@ -203,13 +208,10 @@ TEST_F(MeshcatVisualizerWithIiwaTest, DeletePrefixOnInitialization) {
   }
   // Confirm that my scribble was deleted.
   EXPECT_FALSE(meshcat_->HasPath("/drake/visualizer/my_random_path"));
-  // Confirm that the path that was re-added is again set to be invisible.
-  CheckVisible("/drake/visualizer", false);
 
   // Repeat, but this time with delete prefix disabled.
   params.delete_on_initialization_event = false;
   SetUpDiagram(params);
-  CheckVisible("/drake/visualizer", false);
   meshcat_->SetTransform("/drake/visualizer/my_random_path",
                         math::RigidTransformd());
   {  // Send an initialization event.
@@ -219,7 +221,6 @@ TEST_F(MeshcatVisualizerWithIiwaTest, DeletePrefixOnInitialization) {
   }
   // Confirm that my scribble remains.
   EXPECT_TRUE(meshcat_->HasPath("/drake/visualizer/my_random_path"));
-  CheckVisible("/drake/visualizer", false);
 }
 
 TEST_F(MeshcatVisualizerWithIiwaTest, Delete) {