fix(contrib/aws/datadog-lambda-go): start tracer while initializing lambda listener

[shreyamalpani]

What does this PR do?

Starts the tracer while initializing the lambda listener in instead of on handler started

Tested 50k invocations with a simple Go Lambda handler

Before:

After:

Motivation

SLES-2658 Fast initializing functions hitting timeouts
DataDog/datadog-lambda-go#222

Reviewer's Checklist

• Changed code has unit tests for its functionality at or near 100% coverage.
• System-Tests covering this feature have been added and enabled with the va.b.c-dev version tag.
• There is a benchmark for any new code, or changes to existing code.
• If this interacts with the agent in a new way, a system test has been added.
• New code is free of linting errors. You can check this by running ./scripts/lint.sh locally.
• Add an appropriate team label so this PR gets put in the right place for the release notes.
• Non-trivial go.mod changes, e.g. adding new modules, are reviewed by @DataDog/dd-trace-go-guild.

Unsure? Have a question? Request a review!

[codecov]

Codecov Report

❌ Patch coverage is 0% with 25 lines in your changes missing coverage. Please review.
✅ Project coverage is 55.07%. Comparing base (86c9a30) to head (4062818).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
...b/aws/datadog-lambda-go/internal/trace/listener.go	0.00%	25 Missing ⚠️

Additional details and impacted files

Files with missing lines	Coverage Δ
...b/aws/datadog-lambda-go/internal/trace/listener.go	45.83% <0.00%> (-1.48%)	⬇️

... and 8 files with indirect coverage changes

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[pr-commenter]

Benchmarks

Benchmark execution time: 2026-01-26 20:22:37

Comparing candidate commit 4062818 in PR branch shreya.malpani/fix-lambda-fast-init-issue with baseline commit 86c9a30 in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 157 metrics, 7 unstable metrics.

[shreyamalpani]

/merge

[gh-worker-devflow-routing-ef8351]

View all feedbacks in Devflow UI.

2026-01-26 20:56:53 UTC ℹ️ Start processing command /merge

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2026-01-26 20:57:04 UTC ℹ️ MergeQueue: pull request added to the queue

The expected merge time in main is approximately 43m (p90).

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2026-01-26 21:22:56 UTC ℹ️ MergeQueue: This merge request was merged