diff --git a/muted-tests.yml b/muted-tests.yml
index 41a8da0c63d49..dd0406b6ee40b 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -110,9 +110,6 @@ tests:
   issue: https://github.com/elastic/elasticsearch/issues/120339
 - class: org.elasticsearch.xpack.sql.expression.function.scalar.datetime.DateTimeToCharProcessorTests
   issue: https://github.com/elastic/elasticsearch/issues/120575
-- class: org.elasticsearch.xpack.inference.DefaultEndPointsIT
-  method: testMultipleInferencesTriggeringDownloadAndDeploy
-  issue: https://github.com/elastic/elasticsearch/issues/120668
 - class: org.elasticsearch.xpack.test.rest.XPackRestIT
   method: test {p0=ml/3rd_party_deployment/Test start deployment fails while model download in progress}
   issue: https://github.com/elastic/elasticsearch/issues/120810
diff --git a/x-pack/plugin/inference/qa/inference-service-tests/src/javaRestTest/java/org/elasticsearch/xpack/inference/DefaultEndPointsIT.java b/x-pack/plugin/inference/qa/inference-service-tests/src/javaRestTest/java/org/elasticsearch/xpack/inference/DefaultEndPointsIT.java
index fa6f0b3979653..897a23e5ab13a 100644
--- a/x-pack/plugin/inference/qa/inference-service-tests/src/javaRestTest/java/org/elasticsearch/xpack/inference/DefaultEndPointsIT.java
+++ b/x-pack/plugin/inference/qa/inference-service-tests/src/javaRestTest/java/org/elasticsearch/xpack/inference/DefaultEndPointsIT.java
@@ -25,7 +25,6 @@
 import java.util.concurrent.CountDownLatch;
 
 import static org.hamcrest.Matchers.empty;
-import static org.hamcrest.Matchers.equalTo;
 import static org.hamcrest.Matchers.hasSize;
 import static org.hamcrest.Matchers.is;
 import static org.hamcrest.Matchers.oneOf;
@@ -75,7 +74,7 @@ public void testDefaultModels() throws IOException {
 
         putModel("my-model", mockCompletionServiceModelConfig(TaskType.SPARSE_EMBEDDING, "streaming_completion_test_service"));
         var registeredModels = getMinimalConfigs();
-        assertThat(registeredModels.size(), equalTo(1));
+        assertThat(registeredModels.size(), is(1));
         assertTrue(registeredModels.containsKey("my-model"));
         assertFalse(registeredModels.containsKey(ElasticsearchInternalService.DEFAULT_E5_ID));
         assertFalse(registeredModels.containsKey(ElasticsearchInternalService.DEFAULT_ELSER_ID));
@@ -194,7 +193,14 @@ private static void assertDefaultChunkingSettings(Map<String, Object> modelConfi
         );
     }
 
-    public void testMultipleInferencesTriggeringDownloadAndDeploy() throws InterruptedException {
+    public void testMultipleInferencesTriggeringDownloadAndDeploy() throws InterruptedException, IOException {
+        var initialEndpointId = "initial-model";
+        // Creating an inference endpoint to force the backing indices to be created to reduce the likelihood of the test failing
+        // because it's trying to interact with the indices while they're being created.
+        putModel(initialEndpointId, mockCompletionServiceModelConfig(TaskType.SPARSE_EMBEDDING, "streaming_completion_test_service"));
+        // delete model so it doesn't affect other tests
+        deleteModel(initialEndpointId);
+
         int numParallelRequests = 4;
         var latch = new CountDownLatch(numParallelRequests);
         var errors = new ArrayList<Exception>();